Test Bank For BSTAT 1st Edition by Keller

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BSTAT 1st Edition by Keller – 
Test Bank 

 

CHAPTER 2:  GRAPHICAL AND TABULAR DESCRIPTIVE TECHNIQUES

 

TRUE/FALSE

 

  1. Your age group (1-9; 10-19; 20-29; 30-39; etc.) is an interval variable.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. Your gender is a nominal variable.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Your final grade in a course (A, B, C, D, E) is a nominal variable.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. Your age is an interval variable.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Interval data may be treated as ordinal or nominal.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Whether or not you are over the age of 21 is a nominal variable.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The values of quantitative data are categories.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. Interval data, such as heights, weights, and incomes, are also referred to as quantitative or numerical data.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. All calculations are permitted on interval data.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Nominal data are also called qualitative or categorical data.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A variable is some characteristic of a population or sample.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. With nominal data, there is one and only one way the possible values can be ordered.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. You cannot calculate and interpret differences between numbers assigned to nominal data.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A bar chart is used to represent interval data.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. One of the advantages of a pie chart is that it clearly shows that the total percentages of all the categories add to 100%.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Bar and pie charts are graphical techniques for nominal data. The former focus the attention on the frequency of the occurrences of each category, and the later emphasizes the proportion of occurrences of each category.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A relative frequency distribution lists the categories and their counts.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. A frequency distribution lists the categories and the proportion with which each occurs.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. From a pie chart you are able to find the frequency for each category.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The intervals (classes) in a histogram do not overlap.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The intervals (classes) in a histogram are equally wide.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. In a histogram, each observation is assigned to one or more classes.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The number of class intervals in a histogram depends on the number of observations in the data set.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A relative frequency distribution describes the proportion of data values that fall within each category.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A stem-and-leaf display reveals more information about the original data than does a histogram.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The number of observations within each class may be found in a frequency distribution.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The advantage of a stem-and-leaf display over a histogram is that we can see the actual observations.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. According to the stem-and-leaf plot below, the median quiz score for this data set is 8.

 

Stem-and-leaf of Quiz Score; N = 75
Leaf Unit = 1
9 0 000112333
14 0 56899
21 1 0000123
26 1 66699
33 2 3334445
(8) 2 66677888
34 3 0023344
27 3 56669999
19 4 000122233
10 4 5556667799

 

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. A cumulative relative frequency distribution lists the number of observations that lie below each of the class limits.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. According to the stem-and-leaf plot below, this data set has a negative median.

 

Stem-and-leaf of P/E ratio; N = 75  
Leaf Unit = 0.01  
1 -2 6
2 -2 0
5 -1 555
8 -1 420
22 -0 99999887777665
36 -0 44322111111000
(14) 0 01122233333344
25 0 66678889999
14 1 0022222334
4 1 56
2 2 03

 

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. A histogram represents interval data.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A stem-and-leaf display represents nominal data.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. According to the stem-and-leaf plot below, this data set is symmetric.

 

Stem-and-leaf of P/E ratio; N = 10
Leaf Unit = 0.10
2 -1 53
4 -0 97
(2) -0 65
4 0 3
3 0 6
2 1 3
1 1 8

 

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. When a distribution has more values to the left and tails off to the right, it is skewed negatively.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram the two sides are nearly identical.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A skewed histogram is one with a long tail extending either to the right or left.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. When a distribution has more values to the right and tails to the left, we say it is skewed negatively.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The sum of relative frequencies in a distribution always equals 1.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The sum of cumulative relative frequencies always equals 1.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The original observations cannot be determined once they are grouped into a frequency distribution.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A modal class is the class with the largest number of observations.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Experience shows that few students hand in their statistics exams early; most prefer to hand them in near the end of the test period. This means the time taken by students to write exams is positively skewed.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The graph below is an example of a histogram.

 

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The sum of cumulative relative frequencies always equals 1.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. A line chart is created by plotting the values of the variable on the vertical axis and the time periods on the horizontal axis.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Time series data are often graphically depicted on a line chart, which is a plot of the variable of interest over time.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A line chart that is flat shows no fluctuation in the variable being presented.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The graph below represents a line graph.

 

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. A department store’s monthly sales (in thousands of dollars) for the last year were as follows. A histogram should be used to present these data.

 

Month 1 2 3 4 5 6 7 8 9 10 11 12
Sales 78 74 83 87 85 93 100 105 103 89 78 94

 

 

ANS:   F

 

NAT:   Analytic; Descriptive Statistics

 

  1. The line chart below shows tomato prices each month from January (month 1) to December last year ($ per pound). By looking at this chart you can see the lowest tomato prices occurred in July.

 

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The line chart below shows cucumber prices fluctuated from $2.00 per pound to over $4.50 per pound during the year.

 

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The graphical technique used to describe the relationship between two interval variables is the scatter diagram.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The two most important characteristics revealed by the scatter diagram are the strength and direction of the linear relationship.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Data for calories and salt content (milligrams of sodium) in 17 brands of meat hot dogs are shown in the scatter diagram below. According to this diagram, it appears that hot dogs that are high in sodium are generally low in calories, and hot dogs with low sodium are generally high in calories.

 

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. If we draw a straight line through the points in a scatter diagram and most of the points fall close to the line, there must be a positive relationship between the two variables.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The two most important characteristics to examine in a scatter diagram are the number of possible categories for X and Y and the number of observations in each category.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. When two variables are linearly related, and tend to move in opposite directions, we describe the nature of their association as a negative linear relationship.

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. Correlation implies causation.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. If two variables have a strong linear relationship, that means one variable is causing the other variable to go up or down.

 

ANS:   F                      NAT:   Analytic; Descriptive Statistics

 

  1. The scatter diagram below depicts data with a negative linear relationship.

 

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. The first scatter diagram below shows a stronger linear relationship than the second scatter diagram. (Assume the scales on both scatter diagrams are the same.)

 

 

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

  1. A professor examines the relationship between minutes studying and exam score (out of 200 points) for a random sample of his students. The scatter diagram is shown below. It appears that study time has somewhat of a positive linear relationship with exam score.

 

 

ANS:   T                      NAT:   Analytic; Descriptive Statistics

 

MULTIPLE CHOICE

 

  1. The classification of student major (accounting, economics, management, marketing, other) is an example of a(n)
a. nominal random variable.
b. interval random variable.
c. continuous random variable.
d. parameter.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. The classification of student class designation (freshman, sophomore, junior, senior) is an example of a(n)
a. nominal random variable.
b. interval random variable.
c. ordinal random variable.
d. a parameter.

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. A researcher wishes to estimate the textbook costs of first-year students at Barry University. To do so, he recorded the textbook cost of 300 first-year students and found that their average textbook cost was $195 per semester. The variable of interest to the researcher is
a. textbook cost.
b. class rank.
c. number of students.
d. name of university.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. All calculations are permitted on what type of data?
a. Interval data
b. Nominal data
c. Ordinal data
d. All of these choices are true.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. Values must represent ordered rankings for what type of data?
a. Interval data
b. Nominal data
c. Ordinal data
d. None of these choices.

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. For what type of data are frequencies the only calculations that can be done?
a. Interval data
b. Nominal data
c. Ordinal data
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. For which type of data are the values arbitrary numbers?
a. Interval data
b. Nominal data
c. Ordinal data
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements about pie charts is false?
a. A pie chart is a graphical representation of a relative frequency distribution.
b. You can always determine frequencies for each category by looking at a pie chart.
c. The total percentage of all the slices of a pie chart is 100%.
d. The area of a slice of a pie chart is the proportion of all the individuals that fall into that particular category.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following situations is best suited for a pie chart?
a. The number of dollars spent this year on each type of legal gambling.
b. The percentage of a charitable donation that goes to administrative costs vs. directly to the charity.
c. The number of students in your class who received an A, B, C, D, F on their exam.
d. All of these choices are true.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which situation identifies when to use pie charts and/or bar charts?
a. You want to describe a single set of data.
b. Your data is nominal.
c. You want to show the number or the percentage of individuals in each category.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. Suppose you measure the number of minutes it takes an employee to complete a task, where the maximum allowed time is 5 minutes, and each time is rounded to the nearest minute. Data from 130 employees is summarized below. How long did it take most employees to complete the task?

 

Time (minutes) 1 2 3 4 5
Frequency 25 40 50 35 30

 

a. 5 minutes
b. 3 minutes
c. 30 minutes
d. 50 minutes

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Car buyers were asked to indicate the car dealer they believed offered the best overall service. The four choices were Convoy Motors (C), Mako Chrysler (M), Torrent Auto (T), and Unequaled Chevrolet (U). The following data were obtained:

 

T C C C U C M T C U
U M C M T C M M C M
T C C T U M M C C T
T U C U T M M C U T

 

What percentage of car buyers identified Convoy Motors as having the best overall service?

a. 1/4 = 0.25 or 25%
b. 14/40 = 0.35 or 35%
c. 14%
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following represents a graphical presentation of interval data?
a. A bar chart.
b. A histogram.
c. A pie chart.
d. All of these choices are true.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements about histograms is false?
a. A histogram is a summary of interval data.
b. A histogram is made of a series of intervals, called classes.
c. The classes in a histogram cover the complete range of observations.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements about histograms is false?
a. The intervals of a histogram do not overlap.
b. Every observation is assigned to one and only one class in a histogram.
c. The intervals of a histogram are equally wide.
d. None of these choices.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following describes the shape of the histogram below?

 

 

a. Positively skewed
b. Negatively skewed
c. Symmetric
d. None of these choices

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. The relative frequency of a class in a histogram is computed by
a. dividing the frequency of the class by the number of classes.
b. dividing the frequency of the class by the class width.
c. dividing the frequency of the class by the total of all frequencies.
d. None of these choices.

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. Compare the two histograms below. Which statement is true?

 

 

 

a. The center of histogram A is lower than the center of histogram B.
b. The center of histogram A is higher than the center of histogram B.
c. The center of histogram A is the same as the center of histogram B.
d. You cannot compare the centers of these two histograms without the original data.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. Compare the two histograms below. Which statement is true?

 

 

 

a. The spread of histogram A is smaller than the spread of histogram B.
b. The spread of histogram A is larger than the spread of histogram B.
c. The spread of histogram A is the same as the spread of histogram B.
d. You cannot compare the spreads of these two histograms without the original data.

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. Compare the two histograms below. Which statement is true?

 

 

 

a. The shape of histogram A is the same as the shape of histogram B.
b. The shape of histogram A is positively skewed compared to histogram B.
c. The shape of histogram A is negatively skewed compared to histogram B.
d. You cannot compare the shapes of these two histograms without the original data.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. A modal class in a histogram is the class that includes
a. the largest number of observations.
b. the smallest number of observations.
c. the largest observation in the data set.
d. the smallest observation in the data set.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. The sum of the relative frequencies for all classes in a histogram always equals
a. the number of classes.
b. the class width.
c. the total of all the frequencies.
d. one.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements about shapes of histograms is true?
a. A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size.
b. A negatively skewed histogram is one with a long tail extending to the left.
c. A positively skewed histogram is one with a long tail extending to the right.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. Compare the spread of the two histograms below. Which of the following is true?

 

 

 

a. Data Set A has a larger spread than Data Set B.
b. Data Set A has a smaller spread than Data Set B.
c. Data Set A has the same spread as Data Set B.
d. You cannot compare the spreads of these histograms without the original data.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following is true about a stem-and-leaf display?
a. You can recreate the original data set from it.
b. Its shape resembles a histogram turned on its side.
c. It provides an organized way to depict interval data.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. What does the length of each line of a stem-and-leaf display represent?
a. The percentage of observations in the interval represented by that stem.
b. The number of observations in the interval represented by that stem.
c. The total frequency of observations within or below that stem.
d. The number of digits to the left of the decimal point.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. What values are displayed on a cumulative relative frequency distribution?
a. The number of observations that fall into each class interval.
b. The proportion of observations that fall into each class interval.
c. The number of observations that fall below each class interval.
d. The proportion of observations that fall below each class interval.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. What type of graph depicts the data below?

 

 

a. A line chart
b. A histogram
c. A dot plot
d. A bar chart

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. Observations that are measured at successive points in time is what type of data?
a. Time-series data
b. Cross-sectional data
c. Successive data
d. None of these choices.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. Observations that are measured at the same time represent what type of data?
a. Time-series data
b. Cross-sectional data
c. Synchronous data
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following represents time-series data?
a. The length of time each of the top 100 stocks have been available on the NYSE.
b. The most popular time of year that people purchase the top 100 stocks on the NYSE.
c. The value of the #1 stock on the NYSE each month over a one-year period.
d. All of these choices are true.

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. Time-series data are often graphically depicted how?
a. Bar chart
b. Histogram
c. Line chart
d. All of these choices are true.

 

 

ANS:   C                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements describes a line chart?
a. A line chart is a graph of time-series data.
b. A line chart is a plot of a variable over time.
c. The horizontal axis of a line chart contains time periods.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. What kind(s) of data can be depicted by a line chart?
a. Frequencies of an interval over time.
b. Frequencies of a nominal variable over time.
c. Relative frequencies of a nominal variable over time.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements describe(s) the line chart below?

 

 

a. November experienced the lowest sales throughout the year.
b. August experienced the highest sales throughout the year.
c. Sales did not fluctuate more than 30 units on either side of 90.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. The relationship between two interval variables is graphically displayed by a
a. scatter diagram
b. histogram
c. bar chart
d. pie chart

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. In order to draw a scatter diagram, we need interval data for
a. one variable
b. two variables
c. three variables
d. four variables

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following statements is false?
a. You can examine the relationship between two nominal variables using a cross-classification table.
b. You can only apply statistical techniques to one variable at a time.
c. You can examine the relationship between two interval variables using a scatter diagram.
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. How do you determine whether two interval variables have a positive linear relationship?
a. Most of the points fall close to a straight line with positive slope.
b. As the X variable increases, the Y variable increases in a linear way.
c. The scatter diagram shows a linear pattern that is going uphill.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Descriptive Statistics

 

  1. If the data in a scatter diagram is scattered completely at random, what do you conclude?
a. There is no linear relationship between X and Y.
b. There is a strong linear relationship between X and Y.
c. There is a strong linear relationship between X and Y that is described by a horizontal (flat) line.
d. None of these choices.

 

 

ANS:   A                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following is the method statisticians use to draw the best fitting straight line through the data on a scatter diagram?
a. The fit best method.
b. The least squares method.
c. The point-intercept method.
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. Which of the following describes a positive linear relationship between X and Y?
a. As the X values increase, the Y values increase in a linear manner.
b. As the X values decrease, the Y values decrease in a linear manner.
c. The X and Y values move uphill together in a linear manner.
d. All of these choices are true.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

  1. When two variables tend to move in opposite directions, yet still form a linear pattern, how do you describe their relationship?
a. A positive linear relationship.
b. A negative linear relationship.
c. A proportional inverse relationship.
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Descriptive Statistics

 

COMPLETION

 

  1. The Chief of Police conducted a survey of the officers on his squad. An officer’s shooting score at target practice is an example of a(n) ____________________ variable.

 

ANS:

interval

quantitative

numerical

 

NAT:   Analytic; Descriptive Statistics

 

  1. The Dean of Students conducted a survey on campus. The gender of each student is an example of a(n) ____________________ variable.

 

ANS:

nominal

categorical

qualitative

 

NAT:   Analytic; Descriptive Statistics

 

  1. The Dean of Students conducted a survey on campus. Class rank (Freshman, Sophomore, Junior, and Senior) is an example of a(n) ____________________ variable.

 

ANS:   ordinal

 

NAT:   Analytic; Descriptive Statistics

 

  1. The final grade received in a Literature course (A, B, C, D, or F) is an example of a(n) ____________________ variable.

 

ANS:

nominal

categorical

qualitative

 

NAT:   Analytic; Descriptive Statistics

 

  1. In purchasing a used computer, there are a number of variables to consider. The age of the computer is an example of a(n) ____________________ variable.

 

ANS:

interval

quantitative

numerical

 

NAT:   Analytic; Descriptive Statistics

 

  1. In purchasing an automobile, there are a number of variables to consider. The body style of the car (sedan, coupe, wagon, etc.) is an example of a(n) ____________________ variable.

 

ANS:

nominal

categorical

qualitative

 

NAT:   Analytic; Descriptive Statistics

 

  1. Two types of graphs that organize nominal data are ____________________ and ____________________.

 

ANS:

pie charts; bar charts

bar charts; pie charts

 

NAT:   Analytic; Descriptive Statistics

 

  1. A bar chart is used to represent ____________________ data.

 

ANS:

nominal

categorical

qualitative

 

NAT:   Analytic; Descriptive Statistics

 

  1. A pie chart is used to represent ____________________ data.

 

ANS:

nominal

categorical

qualitative

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ chart is often used to display frequencies; a(n) ____________________ chart graphically shows relative frequencies.

 

ANS:   bar; pie

 

NAT:   Analytic; Descriptive Statistics

 

  1. A pie chart shows the ____________________ of individuals that fall into each category.

 

ANS:

percentage

relative frequency

proportion

 

NAT:   Analytic; Descriptive Statistics

 

  1. We can summarize nominal data in a table that presents the categories and their counts. This table is called a(n) ____________________ distribution.

 

ANS:   frequency

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ distribution lists the categories of a nominal variable and the proportion with which each occurs.

 

ANS:   relative frequency

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ chart is not able to show frequencies. It can only show relative frequencies.

 

ANS:   pie

 

NAT:   Analytic; Descriptive Statistics

 

  1. In a pie chart, each slice is proportional to the ____________________ of individuals in that category.

 

ANS:

percentage

proportion

relative frequency

 

NAT:   Analytic; Descriptive Statistics

 

  1. A category in a pie chart that contains 50% of the observations is represented by a slice of the pie that is equal to ____________________ degrees.

 

ANS:   180

 

NAT:   Analytic; Descriptive Statistics

 

  1. We create a frequency distribution for interval data by counting the number of observations that fall into each of a series of intervals, called ____________________.

 

ANS:   classes

 

NAT:   Analytic; Descriptive Statistics

 

  1. The more observations we have, the ____________________ the number of class intervals we need to use to draw a useful histogram.

 

ANS:

larger

higher

greater

 

NAT:   Analytic; Descriptive Statistics

 

  1. A graph of the frequency distribution for interval data is called a(n) ____________________.

 

ANS:   histogram

 

NAT:   Analytic; Descriptive Statistics

 

  1. We determine the approximate width of the classes of a histogram by subtracting the smallest observation from the largest and dividing the answer by the number of ____________________.

 

ANS:

classes

intervals

 

NAT:   Analytic; Descriptive Statistics

 

  1. A histogram is said to be ____________________ if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size.

 

ANS:

symmetric

symmetrical

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ histogram is one with a long tail extending to either the right or the left.

 

ANS:   skewed

 

NAT:   Analytic; Descriptive Statistics

 

  1. The histogram below has a shape that is ____________________.

 

 

ANS:

symmetric

symmetrical

bell shaped

bell-shaped

 

NAT:   Analytic; Descriptive Statistics

 

  1. It is typical that when taking an exam, few students hand in their exams early; most prefer to reread their papers and hand them in near the end of the scheduled exam period. Under this scenario, a histogram of exam taking times is ____________________ skewed.

 

ANS:   negatively

 

NAT:   Analytic; Descriptive Statistics

 

  1. In a histogram a(n) ____________________ class is the one with the largest number of observations.

 

ANS:   modal

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ histogram has two peaks, not necessarily equal in height.

 

ANS:   bimodal

 

NAT:   Analytic; Descriptive Statistics

 

  1. The length of each line in a step-and-leaf display represents the ____________________ of that class interval defined by the stems.

 

ANS:

frequency

count

 

NAT:   Analytic; Descriptive Statistics

 

  1. The largest value of a cumulative relative frequency is ____________________.

 

ANS:

one

1

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ display shows the actual observations as well as the number of observations in each class.

 

ANS:

stem-and-leaf

stem and leaf

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ is a table that sorts data into class intervals (categories) and gives the number of observations in each interval (category).

 

ANS:   frequency distribution

 

NAT:   Analytic; Descriptive Statistics

 

  1. The line chart below shows potato prices per pound for each month from January (month 1) to December last year. By looking at this chart you can see the lowest potato prices occurred in ____________________.

 

 

ANS:   July

 

NAT:   Analytic; Descriptive Statistics

 

  1. Observations that are measured at the same time are called ____________________ data.

 

ANS:

cross-sectional

cross sectional

 

NAT:   Analytic; Descriptive Statistics

 

  1. Observations that are taken during successive points in time are called ____________________ data.

 

ANS:

time-series

time series

 

NAT:   Analytic; Descriptive Statistics

 

  1. Time series data are often graphically depicted on a(n) ____________________, which is a plot of the variable of interest over time.

 

ANS:   line chart

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ is created by plotting the value of the variable on the vertical axis and the time periods on the horizontal axis.

 

ANS:   line chart

 

NAT:   Analytic; Descriptive Statistics

 

  1. A line chart is created by plotting the value of the variable on the ____________________ axis and the time periods on the ____________________ axis.

 

ANS:

vertical; horizontal

Y; X

 

NAT:   Analytic; Descriptive Statistics

 

  1. In applications involving two variables, X and Y, where one variable depends to some degree on the other, we call Y the ____________________ variable.

 

ANS:   dependent

 

NAT:   Analytic; Descriptive Statistics

 

  1. In applications involving two variables, X and Y, where one variable depends to some degree on the other, we call X the ____________________ variable.

 

ANS:   independent

 

NAT:   Analytic; Descriptive Statistics

 

  1. A(n) ____________________ is a graphical display consisting of a set of points, each point representing one variable measured along the horizontal axis, and another variable measured along the vertical axis.

 

ANS:   scatter diagram

 

NAT:   Analytic; Descriptive Statistics

 

  1. If when one variable increases the other one also increases, we say that there is a(n) ____________________ relationship between these two variables.

 

ANS:

positive

uphill

 

NAT:   Analytic; Descriptive Statistics

 

  1. When one variable increases and the other decreases, we say that there is a(n) ____________________ relationship between these two variables.

 

ANS:

negative

downhill

 

NAT:   Analytic; Descriptive Statistics

 

  1. An individual’s income depends somewhat on their number of years of education. Accordingly, we identify income as the ____________________ variable, and years of education as the ____________________ variable.

 

ANS:

dependent; independent

Y; X

 

NAT:   Analytic; Descriptive Statistics

 

  1. One of the variables used to help predict unemployment rates is the rate of inflation. Accordingly, we identify rate of inflation as the ____________________ variable, and unemployment rate as the ____________________ variable.

 

ANS:

independent; dependent

X; Y

 

NAT:   Analytic; Descriptive Statistics

 

  1. The two most important characteristics to look for in a scatter diagram are the ____________________ and ____________________ of the linear relationship.

 

ANS:

strength; direction

direction; strength

 

NAT:   Analytic; Descriptive Statistics

 

SHORT ANSWER

 

  1. At the end of a safari, the tour guide asks the vacationers to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal.

 

a. How many safaris have you taken prior to this one?
b. Do you feel that your tour safari lasted sufficiently long (yes/no)?
c. Which of the following features of the accommodations did you find most attractive: location, facilities, room size, service, or price?
d. What is the maximum number of hours per day that you would like to spend traveling?
e. Is your overall rating of this safari: excellent, good, fair, or poor?

 

 

ANS:

 

a. Interval
b. Nominal
c. Nominal
d. Interval
e. Ordinal

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. Before leaving a particular restaurant, customers are asked to respond to the questions listed below. For each question, determine whether the possible responses are interval, nominal, or ordinal.

 

a. What is the approximate distance (in miles) between this restaurant and your residence?
b. Have you ever eaten at this restaurant before?
c. On how many occasions have you eaten at the restaurant before?
d. Which of the following attributes of this restaurant do you find most attractive: service, prices, quality of the food, or the menu?
e. What is your overall rating of the restaurant: excellent, good, fair, or poor?

 

 

ANS:

 

a. Interval
b. Nominal
c. Interval
d. Nominal
e. Ordinal

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. For each of the following examples, identify the data type as nominal, ordinal, or interval.

 

a. The final grade received by a student in a neuro-science class.
b. The number of students in a Physics course.
c. The starting salary of a PhD graduate.
d. The size of an order of fries (small, medium, large, super-size) purchased by a Burger King customer.
e. The college you are enrolled in (Arts and Sciences, Business, Education, etc.).

 

 

ANS:

 

a. Ordinal
b. Interval
c. Interval
d. Ordinal
e. Nominal

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. For each of the following, indicate whether the variable of interest is nominal or interval.

 

a. Your marital status.
b. Whether you are a U.S. citizen.
c. Sally’s travel time from her dorm to the student union on campus.
d. The amount of time you spent last week on your homework.
e. The number of cars parked in a certain parking lot at any given time.
f. Kate’s favorite brand of sneakers.

 

 

ANS:

 

a. Nominal
b. Nominal
c. Interval
d. Interval
e. Interval
f. Nominal

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. Provide one example of ordinal data; one example of nominal data; and one example of interval data.

 

ANS:

 

Ordinal data example: Response to a market research survey question measured on the Likert scale using the code: 1 = strongly agree, 2 = agree, 3 = neutral, 4 = disagree, and 5 = strongly disagree.

 

Nominal data example: Voters’ political party affiliation for  using the code: 1 = Democrat, 2 = Republican, and 3 = Independent.

 

Interval data example: The temperature on a golf course during the U.S. Master’s Tournament. (degrees Fahrenheit).

 

NAT:   Analytic; Descriptive Statistics

 

  1. Explain why religious preference is not an ordinal variable.

 

ANS:

The values of religious preference cannot be ranked in order in any way.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Explain the difference between ordinal data and interval data.

 

ANS:

The critical difference between them is that the intervals or differences between values of interval data are consistent and meaningful. That is, we can calculate the difference and interpret the results. Because the codes representing ordinal data are arbitrarily assigned except for the order, we cannot calculate and interpret differences.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Give an example of interval data that can also be treated as ordinal data and nominal data.

 

ANS:

Example: Your actual age is interval data; your age group (1-17; 18-24; 25-30; etc) is ordinal data; and whether or not you are over age 25 is nominal data.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Identify the type of data for which each of the following graphs is appropriate.

 

a. Pie chart
b. Bar chart

 

 

ANS:

 

a. Nominal
b. Nominal

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. Twenty-five voters participating in a recent election exit poll in Minnesota were asked to state their political party affiliation. Coding the data as R for Republican, D for Democrat, and I for Independent, the data collected were as follows: I, R, D, I, R, I, I, D, R, I, I, D, R, R, I, D, I, R, I, D, I, D, R, R, and I. Construct a frequency bar chart from this data. What does the bar chart tell you about the political affiliations of those in this sample?

 

ANS:

 

 

The bar graph shows most of the people surveyed were Independents (11 out of 25 = 44.0%); Republications followed with 8/25 = 32.0% and Democrats made up 6 of the 25, or 24.0%.

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Car Buyers

Car Buyers

 

Forty car buyers were asked to indicate which car dealer offered the best overall service. The four choices were Contour Motors (C), Modern Chrysler (M), Tonneau Auto (T), and Uncanny Chevrolet (U). The following data were obtained:

 

T C C C U C M T C U
U M C M T C M M C M
T C C T U M M C C T
T U C U T M M C U T

 

NARREND

 

 

  1. {Car Buyers Narrative} Construct a frequency bar chart of this data. Which car dealer came in last place in terms of overall service?

 

ANS:

 

 

Uncanny Chevrolet (U) received the fewest votes for best overall service (7 out of 40, or 17.5%) and came in last place.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Car Buyers Narrative} Construct a pie chart of this data. Which car dealer offered the best overall service?

 

ANS:

 

 

Contour Motors (C) received the most votes (35.0%).

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Business School Graduates

Business School Graduates

 

A sample of business school graduates were asked what their major was. The results are shown in the following frequency distribution.

 

Major of Graduates Number of graduates
Accounting 58
Finance 42
Management 38
Marketing 52
Other 10

 

NARREND

 

 

  1. {Business School Graduates Narrative} How many graduates were surveyed?

 

ANS:

200; you get this by totaling the counts for each major.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Business School Graduates Narrative} Draw a pie chart to summarize this data. Which major was the most popular?

 

ANS:

 

 

The most popular major was accounting (29%), followed by marketing (26%).

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Business School Graduates Narrative} Draw a pie chart of this data. Are you able to reconstruct the original data from this pie chart alone?

 

ANS:

 

 

No; you cannot reconstruct the original data from this pie chart alone, because you don’t know how many observations are in each category.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Business School Graduates Narrative} If you were only given the frequency bar chart below, would you able to reconstruct the original observations in the data set?

 

 

ANS:

No; you cannot reconstruct the original data from this graph because the scale on the frequency (Y) axis is not precise enough. For example, you can’t tell exactly what number of students majored in finance; it appears to be 40 on this bar chart, but the actual value is 42, as seen on the original table.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Suppose you measure the number of minutes it takes an employee to complete a task, where the maximum allowed time is 5 minutes, and each time is rounded to the nearest minute. Data from 130 employees is summarized below. Construct a frequency bar chart and a pie chart from this data. How long did it take most employees to complete the task?

 

Time (minutes) 1 2 3 4 5
Frequency 15 30 40 25 20

 

 

ANS:

 

 

The most common time to complete the task was 3 minutes, which was recorded for 40 of the 130 (31%) of the employees.

 

NAT:   Analytic; Descriptive Statistics

 

  1. For what type of data is a histogram appropriate?

 

ANS:

Interval, numerical, or quantitative data.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Twenty-five voters participating in a recent election exit poll in Alabama were asked to state their political party affiliation. Coding the data 1 for Republican, 2 for Democrat, and 3 for Independent, the data collected were as follows: 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3, 2, 3, 1, 3, 2, 3, 2, 1, 1, 3, 1, 2, 2, 1, and 3. Develop a frequency distribution and a relative frequency distribution for this data. What does the data suggest about the strength of the political parties in Alabama?

 

ANS:

 

Party Frequency Proportion
Republican   8 0.33
Democrat   6 0.27
Independent 11 0.40

 

According to the frequency distribution above, the Independents in Alabama outnumber the Republicans and Democrats.

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Teachers Ages

Teachers Ages

 

The ages (in years) of a sample of 25 teachers are as follows:

 

47 21 37 53 28
40 30 32 34 26
34 24 24 35 45
38 35 28 43 45
30 45 31 41 56

 

NARREND

 

 

  1. {Teachers Ages Narrative} Draw a frequency histogram of this data which contains four classes. What is the shape of the histogram?

 

ANS:

 

This histogram of ages of teachers is positively skewed.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Teachers Ages Narrative} Draw a frequency histogram of this data which contains six classes. What is the shape of the histogram?

 

ANS:

*

 

This histogram of ages of teachers is positively skewed.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Teachers Ages Narrative} Draw a stem-and-leaf display of this data. What is the minimum and maximum age of the teachers in this data set?

 

ANS:

 

Stem Leaf
2 144688
3 0012445578
4 0135557
5 36

 

The minimum age is 21 and the maximum age is 56.

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Test Grades

Test Grades

 

The scores on a calculus test for a random sample of 40 students are as follows:

 

63 74 42 65 51 54 36 56 68 57
62 64 76 67 79 61 81 77 59 38
84 68 71 94 71 86 69 75 91 55
48 82 83 54 79 62 68 58 41 47

 

NARREND

 

 

  1. {Test Grades Narrative} Construct a stem-and-leaf display for this data set. Describe the shape of the data.

 

ANS:

 

Stem Leaf
3 68
4 1278
5 14456789
6 12234578889
7 11456799
8 12346
9 14

 

The data is relatively symmetric and bell shaped.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Test Grades Narrative} Construct frequency and relative frequency distributions for this data set using seven class intervals. Describe the shape of the data set.

 

ANS:

 

Class Limits Frequency Relative Frequency
30 to 39   2 0.050
40 to 49   4 0.100
50 to 59   8 0.200
60 to 69 11 0.275
70 to 79   8 0.200
80 to 89   5 0.125
90 to 99   2 0.050
Total 40 1.00

 

The data is relatively symmetric and bell shaped.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Test Grade Narrative} Construct a relative frequency histogram for this data set and discuss its shape.

 

ANS:

 

The distribution of the data is relatively symmetric and bell shaped.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Test Grades Narrative} Describe the distribution of exam scores.

 

ANS:

The distribution of the data is symmetrical and bell-shaped, with 67.5% of the observations between 50 and 80. The center looks to be around 65.

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Test Grades Narrative} Construct a cumulative frequency and a cumulative relative frequency distribution for this data. What proportion of the exam scores are less than 60? What proportion of the exam scores are 70 or more?

 

ANS:

 

Classes Cumulative Cumulative Relative
  Frequency Frequency
< 40   2 0.050
< 50   6 0.150
< 60 14 0.350
< 70 25 0.625
< 80 33 0.825
< 90 38 0.950
  < 100 40 1.000

 

0.35; 1 – 0.625 = 0.375

 

NAT:   Analytic; Descriptive Statistics

 

  1. Forty truck buyers were asked to indicate the car dealer they believed offered the best overall service. The four choices were A, B, C, and D as shown below:

 

A C C C D C B A C D A B C
D B C B A C B B C B B A C
A C C A D B B C C A C D B
A D C D A B B C D A B D A

 

Construct a table showing the frequencies and relative frequencies for this data set. What proportion of car buyers rated dealer D as the best?

 

ANS:

 

Dealer Frequency Relative
    frequency
A 12 0.231
B 14 0.269
C 17 0.327
D   9 0.173

 

0.173 of the truck buyers rated dealer D as the best.

 

NAT:   Analytic; Descriptive Statistics

 

  1. A supermarket’s monthly sales (in thousands of dollars) for the last year were as follows:

 

Month 1 2 3 4 5 6 7 8 9 10 11 12
Sales 78 74 83 87 85 93 100 105 103 89 78 94

 

Construct a relative frequency bar chart for this data set. How many observations are there in this data set?

 

ANS:

See the graph below. There are 12 observations in this data set; one sales amount is listed for each month.

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. Consider the following cumulative frequency distribution.

 

Classes Limits Cumulative Frequency Frequency
< 5 11  
< 10 18  
< 15 24  
< 20 33  
< 25 45  

 

Fill in the frequencies for each class in the above table.

 

ANS:

11; 7; 6; 9; 12

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Insurance Company

Insurance Company

 

A representative from a local insurance agency selected a random sample of insured homeowners and recorded the number of claims made in the last three years, with the following results:

 

Number of claims 0 1 2 3 4 5
Frequency 9 20 14 13 5 3

 

NARREND

 

 

  1. {Insurance Company Narrative} How many homeowners are represented in the sample?

 

ANS:

9 + 20 + 14 + 13 + 5 + 3 = 64

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Insurance Company Narrative} How many total claims are represented in the sample?

 

ANS:

(0 ´ 9) + (1 ´ 20) + (2 ´ 14) + (3 ´ 13) + (4 ´ 5) + (5 ´ 3) = 122

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Insurance Company Narrative} What proportion of homeowners had no claims in the last three years?

 

ANS:

9/64 = .14

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Insurance Company Narrative} What number of claims was made by the highest proportion of homeowners?

 

ANS:

20/64 = 31% of the homeowners had one claim in the last three years.

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Electronics Company

Electronics Company

 

At a meeting of regional offices managers of a national electronics company, a survey was taken to determine the number of employees the regional managers supervise in the operation of their departments. The results of the survey are shown below.

 

Number of employees supervised 1 2 3 4 5
Frequency 7 11 14 8 10

 

NARREND

 

 

  1. {Electronics Company Narrative} How many regional offices are represented in the survey results?

 

ANS:

7 + 11 + 14 + 8 + 10 = 50

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Electronics Company Narrative} Across all of the regional offices, how many total employees were supervised by those surveyed?

 

ANS:

(1 ´ 7) + (2 ´ 11) + (3 ´ 14) + (4 ´ 8) = (5 ´ 10) = 153

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Electronics Company Narrative} What proportion of managers supervise 3 employees?

 

ANS:

14/50 = 0.28

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Electronics Company Narrative} What is the cumulative relative frequency corresponding to 5 employees?

 

ANS:

This is the total proportion of employees supervising 4 or fewer employees: 40/50 = 0.80 or 80%.

 

NAT:   Analytic; Descriptive Statistics

 

NARRBEGIN: Internet Classes

Internet Classes

 

A survey of 25 students was conducted to determine how they rate the quality of Internet classes. Students were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.

 

Stem Leaves
3 15
4 01457889
5 0134677
6 24568
7 29
8  
9 5

 

NARREND

 

 

  1. {Internet Classes Narrative} What percentage of the students rated the overall quality of Internet classes as being 70 or above?

 

ANS:

3/25 = 12%

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Internet Classes Narrative} What percentage of the students rated the overall quality of Internet classes as being 60 or below?

 

ANS:

17/25 = 68%

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Internet Classes Narrative} What percentage of the students rated the overall quality of on-line classes as being between 50 and 75, inclusive?

 

ANS:

13/25 = 52%

 

NAT:   Analytic; Descriptive Statistics

 

  1. {Internet Classes Narrative} What percentage of the students rated the overall quality of on-line classes as being below 40?

 

ANS:

2/25 = 8%

 

NAT:   Analytic; Descriptive Statistics

 

  1. Explain the difference between a histogram and a line chart.

 

ANS:

A histogram is a display of cross-sectional data and a line chart is a display of time-series data.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Briefly discuss the difference between cross-sectional data and time-series data.

 

ANS:

Data can be classified according to whether the observations are measured at the same time or whether they represent measurements at successive points in time. The former are called cross-sectional data and the latter, time-series data.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Beef prices throughout the year (month 1 = January) are shown in the line chart below (per pound). Describe beef prices for this given year using this line chart.

 

 

ANS:

Beef prices started at around $4.50 in January, then lowered consistently through the months of January through July, where they hit their lowest price, $2.00 per pound. Then prices sharply increased until October, and stayed about the same through December. Prices started the year and ended the year at about the same level ($4.50 per pound).

 

NAT:   Analytic; Descriptive Statistics

 

  1. An economics professor wants to study the relationship between income and education. A sample of 10 individuals is selected at random, and their income (in thousands of dollars) and education (in years) are shown below:

 

Education 12 14 10 11 13 8 10 15 13 12
Income 25 31 20 24 28 15 21 35 29 27

 

a. Draw a scatter diagram for these data with the income on the vertical axis.
b. Describe the relationship between income and education.

 

 

ANS:

 

a.  
b. There is a very strong positive linear relationship between education and income; as years of education increase, income also increases in a linear manner.

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. The number of houses sold in Miami Springs and the average monthly mortgage rates for 18 months randomly selected between January 2011 and April 2013 are shown in the following table.

 

Mortgage rate Number of Mortgage rate Number of
(%) houses sold (%) houses sold
  7.5 90   9.5 68
  9.0 72   6.5 97
  7.0 89   8.0 79
10.5 62   9.0 75
10.0 58 10.5 53
  9.5 70   9.5 73
  8.5 74 11.0 50
10.0 65   7.5 82
11.0 51   8.5 70

 

a. Draw a scatter diagram with the number of houses sold on the vertical axis.
b. Describe the relationship between mortgage rate and number of houses sold.

 

 

ANS:

 

a.  
b. There is a strong negative linear relationship between the mortgage rate and the number of houses sold. As the mortgage rate increases, the number of houses sold decreases, in a linear way.

 

 

NAT:   Analytic; Descriptive Statistics

 

  1. Briefly explain the difference between correlation and causation in terms of a relationship between X and Y.

 

ANS:

If two variables are linearly related, it does not mean that one is causing the other to increases or decrease. It means a change in one variable is associated with a change in the other variable, in a linear way. Correlation implies association, not causation.

 

NAT:   Analytic; Descriptive Statistics

 

  1. It is speculated that the number of police officers has a negative linear relationship with number of crimes. Explain why this might be so.

 

ANS:

As the number of police offers increases, number of crimes goes down. As the number of police officers decreases, the number of crimes goes up.

 

NAT:   Analytic; Descriptive Statistics

 

  1. What are the two most important characteristics to look for in a scatter diagram?

 

ANS:

The strength and direction of the linear relationship between the two variables.

 

NAT:   Analytic; Descriptive Statistics

 

  1. Can a scatter diagram be used to explore the relationship between two nominal variables? Explain why or why not.

 

ANS:

No; scatter diagrams plot points of X and Y when both variables are interval variables. You cannot talk about a nominal variable increasing or decreasing.

 

NAT:   Analytic; Descriptive Statistics

 

CHAPTER 4:  DATA COLLECTION AND SAMPLING

 

TRUE/FALSE

 

  1. An observational study involves collecting data about persons or objects by recording information about their selected characteristics of interest.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Self-administered surveys usually have a high response rate.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. In designing a survey, demographic questions must be avoided.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. The response rate of a survey is the proportion of all people who were selected but did not complete the survey.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. A self-selected sample is the group of individuals who were randomly selected to be in the sample, then agreed to participate in the study.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. Experimental data tend to be more reliable, or “stronger,” than survey data.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. An experiment involves collecting data about persons or objects by deliberately exposing them to some kind of change and comparing the results.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. A question on a survey that was not answered is an example of an open-ended question.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. A self-selected sample is one in which the individuals choose themselves to be in the sample.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. “Wouldn’t you agree that foreign cars are better than American cars?” is an example of a well-worded survey question.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. A person receives a mail survey and shreds it without opening it. This causes nonresponse error.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Self-selected samples have no bias because they are chosen by the people themselves.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. A cluster sample occurs when you randomly select groups, and for each group selected, you sample every single member of that group.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. The larger the sample size is, the more accurate we can expect our sample estimates to be.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Selection bias occurs when researchers select biased questions to include on a survey.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. The target population is the population about which we want to draw inferences and conclusions, while the sampled population is the actual population from which the sample has been taken.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. A target population and a sampled population mean the same thing.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. A self-selected sample represents the sampled population but not the target population.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. A nonsampling error can be caused by the wording of a question.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. When responses are not obtained from some members of the sample, bias is introduced.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. A sampling error can be reduced by taking a larger sample size.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Sampling error refers to the difference between the sample and the population that exists only because of the observations that happened to be selected for the sample by chance.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Sampling error is the result of a mistake made during the sampling process.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. Cluster samples typically cost less but they also increase sampling error.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. A simple random sample is chosen in such a fashion that every possible subset of the same size has an equal chance of being selected.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Nonresponse error occurs when responses are not obtained from some members of the sample.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. Nonresponse error occurs when someone was not selected to participate in the survey.

 

ANS:   F                      NAT:   Analytic; Sampling

 

  1. Selection bias is a systematic tendency to favor including individuals with particular characteristics, while excluding individuals with other characteristics.

 

ANS:   T                      NAT:   Analytic; Sampling

 

  1. To reduce sampling error, minimize the chance for bias to occur during sampling.

 

ANS:   F                      NAT:   Analytic; Sampling

 

MULTIPLE CHOICE

 

  1. Which method of data collection is involved when a researcher counts and records the number of students wearing backpacks on campus in a given day?
a. An experiment.
b. A survey.
c. Direct observation.
d. None of these choices.

 

 

ANS:   C                     NAT:   Analytic; Sampling

 

  1. Which of the following statements is true regarding the design of a good survey?
a. The questions should be kept as short as possible.
b. A mixture of dichotomous, multiple-choice, and open-ended questions may be used.
c. Leading questions must be avoided.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Sampling

 

  1. A marketing research firm selects a random sample of adults and asks them a list of questions regarding their beverage preferences. What type of data collection is involved here?
a. An experiment.
b. A survey.
c. Direct observation.
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Sampling

 

  1. Which of the following must be avoided in designing a survey?
a. Dichotomous questions.
b. Leading questions.
c. Demographic questions.
d. All of these choices are true.

 

 

ANS:   B                     NAT:   Analytic; Sampling

 

  1. A researcher conducts a study where she divides subjects into two groups, gives each group a certain treatment, and records their responses. What type of data collection is being used here?
a. An experiment.
b. Direct observation.
c. A survey.
d. A census.

 

 

ANS:   A                     NAT:   Analytic; Sampling

 

  1. The personnel director at a large company studied the eating habits of the company’s employees. The director watched and recorded whether each employee brought his/her own lunch to work, ate at the company cafeteria, or went out to lunch. What method of data collection was used here?
a. Direct observation.
b. An experiment.
c. A survey.
d. A personal interview.

 

 

ANS:   A                     NAT:   Analytic; Sampling

 

  1. Which of the following data collection methods is not observational?
a. A personal interview.
b. A telephone interview.
c. A self-administered questionnaire.
d. An experiment.

 

 

ANS:   D                     NAT:   Analytic; Sampling

 

  1. When every possible sample with the same number of observations is equally likely to be chosen, the result is called a:
a. simple random sample.
b. stratified random sample.
c. cluster sample.
d. biased sample.

 

 

ANS:   A                     NAT:   Analytic; Sampling

 

  1. The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a:
a. simple random sample.
b. stratified random sample.
c. cluster sample.
d. self-selected sample.

 

 

ANS:   B                     NAT:   Analytic; Sampling

 

  1. Which of the following causes sampling error?
a. Taking a random sample from a population instead of studying the entire population.
b. Making a mistake in the process of collecting the data.
c. Nonresponse bias.
d. All of these choices are true.

 

 

ANS:   A                     NAT:   Analytic; Sampling

 

  1. A pharmaceutical company interested in measuring how often physicians prescribe a certain drug has selected a simple random sample from each of two groups: M.D. (Medical Doctors) and D.O. (Osteopaths). What is this type of sampling called?
a. Simple random sampling.
b. Cluster sampling.
c. Stratified random sampling.
d. None of these choices.

 

 

ANS:   C                     NAT:   Analytic; Sampling

 

  1. When the population is divided into mutually exclusive sets, and then a simple random sample is drawn from each set, this is called:
a. simple random sampling.
b. stratified random sampling.
c. cluster sampling.
d. selection bias.

 

 

ANS:   B                     NAT:   Analytic; Sampling

 

  1. Which of the following types of samples is almost always biased?
a. Simple random samples.
b. Stratified random samples.
c. Cluster samples.
d. Self-selected samples.

 

 

ANS:   D                     NAT:   Analytic; Sampling

 

  1. The difference between a sample mean and the population mean is called:
a. nonresponse error.
b. selection bias.
c. sampling error.
d. nonsampling error.

 

 

ANS:   C                     NAT:   Analytic; Sampling

 

  1. Which of the following types of samples should not be used to make good statistical inferences from a sample to a population?
a. Stratified random samples.
b. Self-selected samples.
c. Cluster samples.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Sampling

 

  1. Which of the following is an example of a nonsampling error?
a. Some incorrect responses are recorded.
b. Responses are not obtained from all members of the sample.
c. Some members of the target population cannot possibly be selected for the sample.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Sampling

 

  1. The Admissions Officer from a large university mailed a survey to 600 students selected at random. The sample was designed to include 150 students randomly selected from each of the freshman, sophomore, junior, and senior classes on campus. What sampling method was used?
a. Simple random sample
b. Systematic sample
c. Stratified random sample
d. Cluster sample

 

 

ANS:   C                     NAT:   Analytic; Sampling

 

  1. Which of the following situations lends itself to cluster samples?
a. When it is difficult to develop a complete list of the population members.
b. When the population members are widely dispersed.
c. When selecting and collecting data from a simple random sample is too costly.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Sampling

 

  1. To give away a door prize, the hostess of a Tupperware party put each person’s name into a hat, mixed them up, and selected one name. What sampling method was used?
a. Simple random sample
b. Systematic sample
c. Stratified random sample
d. Cluster sample

 

 

ANS:   A                     NAT:   Analytic; Sampling

 

  1. Which of the following describes selection bias?
a. A leading question is selected for inclusion in the survey.
b. Some members of the target population are excluded from possible selection for the sample.
c. A person selected for the sample has a biased opinion about the survey.
d. All of these choices are true.

 

 

ANS:   B                     NAT:   Analytic; Sampling

 

COMPLETION

 

  1. In a(n) ____________________ study, there is no attempt to control factors that might influence the variable of interest.

 

ANS:   observational

 

NAT:   Analytic; Sampling

 

  1. The ____________________ rate is the proportion of people in the sample who completed the survey.

 

ANS:   response

 

NAT:   Analytic; Sampling

 

  1. In a(n) ____________________ study, individuals are randomly assigned to different treatments and the results are compared.

 

ANS:   experimental

 

NAT:   Analytic; Sampling

 

  1. A survey is an example of a(n) ____________________ study.

 

ANS:   observational

 

NAT:   Analytic; Sampling

 

  1. Two types of interviews that are used to collect data are ____________________ interviews and ____________________ interviews.

 

ANS:

personal; telephone

telephone; personal

 

NAT:   Analytic; Sampling

 

  1. In a self-administered survey, the individuals in the sample are typically contacted by ____________________.

 

ANS:   mail

 

NAT:   Analytic; Sampling

 

  1. Gender, occupation, and age are all examples of ____________________ variables.

 

ANS:   demographic

 

NAT:   Analytic; Sampling

 

  1. Proper interviewer training helps to reduce ____________________ error.

 

ANS:   nonsampling

 

NAT:   Analytic; Sampling

 

  1. Excluding some members of the target population results in ____________________ bias.

 

ANS:   selection

 

NAT:   Analytic; Sampling

 

  1. ____________________ error results from the failure to collect data from all subjects in the sample.

 

ANS:   Nonresponse

 

NAT:   Analytic; Sampling

 

  1. ____________________ error refers to differences between the sample and the population.

 

ANS:   Sampling

 

NAT:   Analytic; Sampling

 

  1. ____________________ error is due to mistakes made in the acquisition of data.

 

ANS:   Nonsampling

 

NAT:   Analytic; Sampling

 

  1. A(n) ____________________ sample is obtained by separating the population into groups and taking a simple random sample from each group.

 

ANS:

stratified

stratified random

 

NAT:   Analytic; Sampling

 

  1. ____________________ sampling is particularly useful when it is difficult or costly to develop a complete list of the population members.

 

ANS:   Cluster

 

NAT:   Analytic; Sampling

 

SHORT ANSWER

 

  1. Describe the difference between an observational study and an experimental study.

 

ANS:

In an observational study, there is no attempt to control factors that might influence the variable of interest. In an experimental study, a factor (such as regular use of fitness center) is controlled by randomly selecting who is exposed to that factor, thereby reducing the influence of other factors on the variable of interest.

 

NAT:   Analytic; Sampling

 

  1. Briefly discuss three methods of conducting a survey of people.

 

ANS:

 

a. Personal interview: involves an interviewer soliciting information from a respondent by asking prepared questions; it has a higher expected response rate but is typically expensive.
b. Telephone interview: involves soliciting information by calling people. This is usually less expensive, but it is also less personal and has a lower expected response rate.
c. Self-administered survey: this is an inexpensive method of conducting a survey which is usually mailed to a sample of people; it usually has a very low response rate.

 

 

NAT:   Analytic; Sampling

 

  1. Give three important points to consider when designing a questionnaire.

 

ANS:

Any three of the following are acceptable:

 

a. Keep the questionnaire as short as possible.
b. Design the questions to be short, simple, and clearly worded.
c. Consider beginning with simple demographic questions to help respondents get started and become comfortable quickly.
d. Consider using a combination of dichotomous questions, multiple-choice questions, and open-ended questions.
e. Avoid using leading questions.
f. When preparing the questions, think about how you intend to tabulate and analyze the responses.

 

 

NAT:   Analytic; Sampling

 

  1. List one advantage and one disadvantage of a telephone interview as a method of data collection.

 

ANS:

Advantage: It is usually less expensive than other methods of data collection.

 

Disadvantages: It is less personal, has a lower expected response rate, and many people will refuse to respond to telephone surveys unless the issue is of interest to them.

 

NAT:   Analytic; Sampling

 

  1. List one advantage and one disadvantage of a personal interview as a method of data collection.

 

ANS:

Advantages: It has a higher expected response rate than other methods of data collection. In addition, there will probably be fewer incorrect responses resulting from respondents misunderstanding some questions, because the interviewer, if asked, can clarify misunderstandings.

 

Disadvantages: It has the potential for bias if the interviewer says too much whenever asked to clarify misunderstandings of some questions. The main disadvantage of personal interviews is that they are expensive, especially when travel is involved.

 

NAT:   Analytic; Sampling

 

  1. Discuss one advantage and one disadvantage of a self-administered survey as a method of data collection.

 

ANS:

Advantages: It is an inexpensive method of conducting a survey, since it is usually mailed to a sample of people, and is therefore attractive when the number of people to be surveyed is large.

 

Disadvantages: Self-administered surveys usually have low response rates and may have a relatively high number of incorrect responses due to respondents misunderstanding some questions.

 

NAT:   Analytic; Sampling

 

NARRBEGIN: Soft Drinks

Soft Drinks

 

A soft drink manufacturer has been supplying its products in bottles to grocery stores and in cans to small convenience stores. The company is analyzing sales of this product to determine which type of packaging is preferred by customers.

NARREND

 

 

  1. {Soft Drink Narrative} Is this study observational or experimental? Explain.

 

ANS:

The study is observational. The statistics practitioner did not randomly assign stores to selling bottles or cans. Type of store and type of packaging cannot be separated here.

 

NAT:   Analytic; Sampling

 

  1. {Soft Drink Narrative} Outline a better method for designing this study, so the same types of stores don’t get the same types of packaging.

 

ANS:

Randomly assign some grocery stores to receive bottles and the other grocery stores to receive cans. Randomly assign some convenience stores to receive bottles and the other convenience stores to receive cans. Or, have each store (convenience or grocery) carry both bottles and cans.

 

NAT:   Analytic; Sampling

 

NARRBEGIN: Smoking and Heart Attacks

Smoking and Heart Attacks

 

A medical researcher is interested in investigating the relationship between smoking and heart attacks

NARREND

 

 

  1. {Smoking and Heart Attacks Narrative} Briefly describe how the researcher might design an observational study to investigate the relationship between smoking and heart attacks

 

ANS:

Randomly sample a group of smokers and randomly sample a group of nonsmokers. Follow these individuals and find the proportion of each group that has a heart attack. Or, sample a group of individuals that had a heart attack and find out what proportion of them smoked and what proportion did not smoke.

 

NAT:   Analytic; Sampling

 

  1. {Smoking and Heart Attacks Narrative} What type of studies are plausible in this particular scenario, observational studies or experiments?

 

ANS:

Observational studies are the only choice here. Experimental data would require the medical researcher to randomly assign some people to smoke and others not to smoke. This of course is not ethical.

 

NAT:   Analytic; Sampling

 

  1. {Smoking and Heart Attacks Narrative} How can you show that smoking causes heart attacks without being able to do a designed experiment?

 

ANS:

Instead of conducting one simple observational study, conduct many observational studies, each looking at smoking and heart attacks from a different angle, for all different populations. Once the entire body of evidence from all these studies is examined, the connection can be seen between smoking and heart attacks.

 

NAT:   Analytic; Sampling

 

  1. What is meant by a self-selected sample? Why are self-selected samples not desirable?

 

ANS:

A self-selected sample is a sample formed primarily on the basis of voluntary inclusion, with little control by the designer of the survey. Self-selected samples are usually biased, because those who participate are more interested in the issue than those who don’t, and therefore probably have a different opinion.

 

NAT:   Analytic; Sampling

 

  1. A senator wants to estimate the mean age of registered voters in her state. Unfortunately, she does not have a complete list of households in her state. Describe a sampling plan that would be suitable for her purposes.

 

ANS:

Use cluster sampling, where each city block is a cluster. Select a certain number of state counties at random, then for each city block selected, sample each household in that county.

 

NAT:   Analytic; Sampling

 

  1. The Chairman of a College of Business with five departments wants to estimate the average number of student-hours lost per month due to illness of their professors. Describe a sampling plan that will help the Dean compare the average student-loss hours for the five departments.

 

ANS:

The Chairman can take one simple random sample from each department for comparison purposes. That means he is taking a stratified random sample, where the strata are the five departments.

 

NAT:   Analytic; Sampling

 

  1. Briefly describe three types of nonsampling errors.

 

ANS:

 

a. Errors in data acquisition: Errors that arise from the recording of incorrect responses.
b. Nonresponse error: Errors that arise when responses are not obtained from some members of the sample.
c. Selection bias: Errors that arise when some members of the target population cannot possibly be selected for the sample.

 

 

NAT:   Analytic; Sampling

 

  1. Pollsters want to know what percentage of all registered voters in Missoula, Montana, intend to vote in the next election. They visit with 350 people at the downtown shopping mall during one afternoon and ask each person whether or not they intend to vote. Are the target population and the sampled population the same in this case? Explain.

 

ANS:

In this situation, the target population and the sampled population are not the same. The target population consists of all registered voters in Missoula, Montana. The sampled population, however, consists of anyone in Missoula who was at that mall that afternoon (registered voters or not), thereby excluding a very large portion of the Missoula, Montana, registered voters.

 

NAT:   Analytic; Sampling

 

  1. Give an example of a poll that involves a self-selected sample.

 

ANS:

Choose any recent radio or television poll based on responses of listeners who phone in on a volunteer basis. Another example is a survey that appears on an Internet website.

 

NAT:   Analytic; Sampling

 

  1. Is it possible for a sample to yield better results than a census, from a practical standpoint? Explain.

 

ANS:

Yes. In any case where the population is large in size, a census will likely contain significantly more nonsampling errors than a carefully conducted sample survey.

 

NAT:   Analytic; Sampling

 

  1. A regular feature in many newspapers asks readers to respond via e-mail to a survey question. The percentages of yes and no responses are usually reported the following day. Should we ignore the results of these surveys? Explain.

 

ANS:

Yes, we should ignore the results because this is an example of a self-selected sample. Self-selected samples are almost always biased because they tend to only represent those with strong opinions.

 

NAT:   Analytic; Sampling

CHAPTER 9:  INTRODUCTION TO ESTIMATION

 

TRUE/FALSE

 

  1. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. An unbiased estimator is a sample statistic whose expected value equals the population parameter.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows larger as the sample size grows larger.

 

ANS:   F                      NAT:   Analytic; Interval Estimation

 

  1. If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. An interval estimate is a range of values within which the actual value of the population parameter, such as m, may fall.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. An interval estimate is an estimate of the range for a sample statistic.

 

ANS:   F                      NAT:   Analytic; Interval Estimation

 

  1. The sample variance (where you divide by n – 1) is an unbiased estimator of the population variance.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. The sample mean  is a consistent estimator of the population mean m.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. The sample proportion  is a consistent estimator of the population proportion p because it is unbiased and the variance of  is p(1 – p) / n, which grows smaller as n grows larger.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. The sample variance s2 is an unbiased estimator of the population variance s2 when the denominator of s2 is n.

 

ANS:   F                      NAT:   Analytic; Interval Estimation

 

  1. An unbiased estimator has an average value (across all samples) equal to the population parameter.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. The sample variance is a point estimate of the population variance.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. The confidence interval estimate of the population mean is constructed around the sample mean.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

 

ANS:   T                      NAT:   Analytic; Interval Estimation

 

  1. A specific confidence interval obtained from data will always correctly estimate the population parameter.

 

ANS:   F                      NAT:   Analytic; Interval Estimation

 

  1. In determining the sample size needed to estimate the population proportion p, we let the sample proportion  = 1 if we have no knowledge of even the approximate values of .

 

ANS:   F                      NAT:   Analytic; Hypothesis Testing

 

  1. The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and  = 0.10, is 0.0247.

 

ANS:   F                      NAT:   Analytic; Hypothesis Testing

 

  1. The sampling distribution of  is approximately normal if the sample size is more than 30.

 

ANS:   F                      NAT:   Analytic; Hypothesis Testing

 

  1. In testing a hypothesis about a population proportion p, the z test statistic measures how close the computed sample proportion  has come to the hypothesized population parameter.

 

ANS:   T                      NAT:   Analytic; Hypothesis Testing

 

  1. If we have some idea about the value of sample proportion , we use that value in determining the sample size needed to estimate the population proportion p.

 

ANS:   T                      NAT:   Analytic; Hypothesis Testing

 

  1. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

 

ANS:   F                      NAT:   Analytic; Hypothesis Testing

 

MULTIPLE CHOICE

 

  1. An estimator is said to be consistent if:
a. the difference between the estimator and the population parameter grows smaller as the sample size grows larger.
b. it is an unbiased estimator.
c. the variance of the estimator is zero.
d. the difference between the estimator and the population parameter stays the same as the sample size grows larger.

 

 

ANS:   A                     NAT:   Analytic; Interval Estimation

 

  1. A point estimator is defined as:
a. a range of values that estimates an unknown population parameter.
b. a single value that estimates an unknown population parameter.
c. a range of values that estimates an unknown sample statistic.
d. a single value that estimates an unknown sample statistic.

 

 

ANS:   B                     NAT:   Analytic; Interval Estimation

 

  1. Which of the following is not a characteristic for a good estimator?
a. Being unbiased
b. Being consistent
c. Having relative efficiency
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Interval Estimation

 

  1. An unbiased estimator of a population parameter is defined as:
a. an estimator whose expected value is equal to the parameter.
b. an estimator whose variance is equal to one.
c. an estimator whose expected value is equal to zero.
d. an estimator whose variance goes to zero as the sample size goes to infinity.

 

 

ANS:   A                     NAT:   Analytic; Interval Estimation

 

  1. Which of the following statements is true?
a. The sample mean is relatively more efficient than the sample median.
b. The version of the sample variance where you divide by n is biased.
c. The sample mean is consistent.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Interval Estimation

 

  1. Which of the following statements is correct?
a. The sample mean is an unbiased estimator of the population mean.
b. The sample proportion is an unbiased estimator of the population proportion.
c. The difference between two sample means is an unbiased estimator of the difference between two population means.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Interval Estimation

 

  1. If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be:
a. a biased estimator.
b. relatively efficient.
c. consistent.
d. relatively unbiased.

 

 

ANS:   B                     NAT:   Analytic; Interval Estimation

 

  1. The problem with relying on a point estimate of a population parameter is that:
a. it is virtually certain to be wrong.
b. it doesn’t have the capacity to reflect the effects of larger sample sizes.
c. it doesn’t tell us how close or far the point estimate might be from the parameter.
d. All of these choices are true.

 

 

ANS:   D                     NAT:   Analytic; Interval Estimation

 

  1. The sample variance s2 is an unbiased estimator of the population variance s2 when the denominator of s2 is
a. n + 1
b. n
c. n – 1
d.

 

 

ANS:   C                     NAT:   Analytic; Interval Estimation

 

  1. The librarian at the New York City Public Library has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant took a sample and found the mean to be 880 books. She provides the librarian with an interval estimate of between 790 and 970 books checked out per day. An efficient, unbiased point estimate of the number of books checked out each day at the New York City Public Library is:
a. 790
b. 880
c. 90
d. None of these choices.

 

 

ANS:   B                     NAT:   Analytic; Interval Estimation

 

  1. In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion , we:
a. take another sample and estimate .
b. take two more samples and find the average of their .
c. let  = 0.50.
d. let  = 0.95.

 

 

ANS:   C                     NAT:   Analytic; Hypothesis Testing

 

  1. Under what condition(s) does the test statistic for p have an approximate normal distribution?
a. When np > 5.
b. When np and np(1 – p) are both > 5.
c. When n > 30.
d. When np and n(1 – p) are both > 5.

 

 

ANS:   D                     NAT:   Analytic; Hypothesis Testing

 

  1. The use of the standard normal distribution for constructing confidence interval estimate for the population proportion p requires:
a. n and n(1 – ) both greater than 5.
b. np and n(1 – p) both greater than 5.
c. n(1 + ) and n(1 – ) both greater than 5.
d. sample size greater than 5.

 

 

ANS:   A                     NAT:   Analytic; Hypothesis Testing

 

  1. After calculating the sample size needed to estimate a population proportion to within 0.04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led to a sample size of 800, the sample size will now have to be:
a. 800
b. 3,200
c. 6,400
d. 12,800

 

 

ANS:   D                     NAT:   Analytic; Hypothesis Testing

 

  1. Assuming that all necessary conditions are met, what needs to be changed in the formula  so that we can use it to construct a (1 – a) confidence interval estimate for the population proportion p?
a.  should be replaced by p.
b. ta should be replaced by za.
c. ta should be replaced by ta / 2.
d. ta should be replaced by za / 2.

 

 

ANS:   D                     NAT:   Analytic; Hypothesis Testing

 

  1. The width of a confidence interval estimate for a proportion will be:
a. narrower for 90% confidence than for 95% confidence.
b. wider for a sample size of 100 than for a sample size of 50.
c. narrower for 99% confidence than for 95% confidence.
d. narrower when the sample proportion if 0.50 than when the sample proportion is 0.20.

 

 

ANS:   A                     NAT:   Analytic; Hypothesis Testing

 

  1. When determining the sample size needed for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be:
a. the smaller the sample size required.
b. the larger the sample size required.
c. the sample size is not affected.
d. the effect cannot be determined from the information given.

 

 

ANS:   B                     NAT:   Analytic; Hypothesis Testing

 

  1. Which of the following would be an appropriate null hypothesis?
a. The population proportion is equal to 0.60.
b. The sample proportion is equal to 0.60.
c. The population proportion is not equal to 0.60.
d. All of these choices are true.

 

 

ANS:   A                     NAT:   Analytic; Hypothesis Testing

 

  1. Which of the following would be an appropriate alternative hypothesis?
a. The population proportion is less than 0.65.
b. The sample proportion is less than 0.65.
c. The population proportion is equal to 0.65.
d. The sample proportion is equal to 0.65.

 

 

ANS:   A                     NAT:   Analytic; Hypothesis Testing

 

  1. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors’ results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:
a. -1.67
b. -2.33
c. -1.86
d. -0.14

 

 

ANS:   B                     NAT:   Analytic; Hypothesis Testing

 

  1. From a sample of 400 items, 14 are found to be defective. The point estimate of the population proportion defective will be:
a. 0.035
b. 0.05
c. 14
d. 28.57

 

 

ANS:   A                     NAT:   Analytic; Hypothesis Testing

 

COMPLETION

 

  1. It is intuitively reasonable to expect that a larger sample will produce more ____________________ results.

 

ANS:

accurate

precise

 

NAT:   Analytic; Interval Estimation

 

  1. ____________________ estimators do not have the capacity to reflect the effects of larger sample sizes.

 

ANS:   Point

 

NAT:   Analytic; Interval Estimation

 

  1. ____________________ estimators reflect the effects of larger sample sizes, but ____________________ estimators do not.

 

ANS:   Interval; point

 

NAT:   Analytic; Interval Estimation

 

  1. An interval estimator estimates the value of an unknown ____________________.

 

ANS:   parameter

 

NAT:   Analytic; Interval Estimation

 

  1. A(n) ____________________ estimator of a population parameter is an estimator whose expected value is equal to that parameter.

 

ANS:   unbiased

 

NAT:   Analytic; Interval Estimation

 

  1. The sample ____________________ is an unbiased estimator for the population mean.

 

ANS:

mean

average

 

NAT:   Analytic; Interval Estimation

 

  1. The version of the sample variance where you divide by ____________________ gives you an unbiased estimator of the population variance.

 

ANS:

n – 1

n-1

 

NAT:   Analytic; Interval Estimation

 

  1. An unbiased estimator is ____________________ if its variance gets smaller as n gets larger.

 

ANS:   consistent

 

NAT:   Analytic; Interval Estimation

 

  1. If there are two unbiased estimators of the same parameter, the one whose variance is smaller is said to be relatively more ____________________.

 

ANS:   efficient

 

NAT:   Analytic; Interval Estimation

 

  1. The sample ____________________ is relatively more efficient than the sample ____________________ when estimating the population mean.

 

ANS:

mean; median

average; median

 

NAT:   Analytic; Interval Estimation

 

  1. Estimating or testing for p is used in situations when the data are ____________________.

 

ANS:   nominal

 

NAT:   Analytic; Hypothesis Testing

 

  1. The test statistic for p is approximately normal when ____________________ and ____________________ are both greater than 5.

 

ANS:

np; n(1 – p)

n(1 – p); np

np; n(1-p)

n(1-p); np

 

NAT:   Analytic; Hypothesis Testing

 

  1. The test statistic for p is approximately normal when np and n(1 – p) are both ____________________.

 

ANS:

greater than 5

> 5

 

NAT:   Analytic; Hypothesis Testing

 

  1. When a population is small, it is necessary to include the ____________________ factor in our hypothesis tests and confidence interval estimators for p.

 

ANS:   finite population correction

 

NAT:   Analytic; Hypothesis Testing

 

  1. To produce a confidence interval estimator for the total, we multiply the lower and upper confidence limits of the interval estimator of p by ____________________.

 

ANS:

N

the population size

 

NAT:   Analytic; Hypothesis Testing

 

  1. The formula  is used to find the ____________________ to estimate a population proportion.

 

ANS:   sample size

 

NAT:   Analytic; Hypothesis Testing

 

  1. The formula is used to find the sample size needed to estimate a population proportion. In this formula, B represents the ____________________ on the error of estimation.

 

ANS:   bound

 

NAT:   Analytic; Hypothesis Testing

 

  1. The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

 

ANS:   error; estimation

 

NAT:   Analytic; Interval Estimation

 

  1. The error of estimation is the ____________________ between an estimator and the parameter.

 

ANS:

difference

distance

 

NAT:   Analytic; Interval Estimation

 

  1. When determining the required sample size for a confidence interval, you need to know the population ____________________, the confidence ____________________, and the ____________________ on the error of estimation.

 

ANS:   standard deviation; level; bound

 

NAT:   Analytic; Interval Estimation

 

  1. Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

 

ANS:   up

 

NAT:   Analytic; Interval Estimation

 

  1. If the bound on the error of estimation decreases, the sample size ____________________.

 

ANS:   increases

 

NAT:   Analytic; Interval Estimation

 

  1. If the population standard deviation is guesstimated, and it turned out to be smaller than you assumed, then the sample size you calculated is ____________________ than it needs to be.

 

ANS:

larger

bigger

greater

more

 

NAT:   Analytic; Interval Estimation

 

  1. If the population standard deviation is guesstimated, and it turned out to be larger than you assumed, then the sample size you calculated is ____________________ than it needs to be.

 

ANS:

smaller

less

 

NAT:   Analytic; Interval Estimation

 

  1. Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

 

ANS:   width

 

NAT:   Analytic; Interval Estimation

 

  1. The bound on the error of estimation is the ____________________ amount of sampling error that we are willing to tolerate.

 

ANS:

maximum

greatest

largest

 

NAT:   Analytic; Interval Estimation

 

  1. As the bound on the error of estimation decreases, the sample size ____________________.

 

ANS:   increases

 

NAT:   Analytic; Interval Estimation

 

SHORT ANSWER

 

  1. Define unbiasedness.

 

ANS:

An unbiased estimator of a parameter is an estimator whose expected value equals the parameter.

 

NAT:   Analytic; Interval Estimation

 

  1. Define consistency.

 

ANS:

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

 

NAT:   Analytic; Interval Estimation

 

  1. Is the sample mean a consistent estimator of the population mean? Explain

 

ANS:

Yes, the mean is consistent because it is unbiased and the standard error grows smaller as the sample size n increases.

 

NAT:   Analytic; Interval Estimation

 

  1. Draw a sampling distribution of an unbiased estimator for m.

 

ANS:

 

NAT:   Analytic; Interval Estimation

 

  1. Draw a sampling distribution of a biased estimator for m.

 

ANS:

 

NAT:   Analytic; Interval Estimation

 

  1. Draw sampling distributions of a consistent estimator for m where one sample mean is larger than the other.

 

ANS:

 

NAT:   Analytic; Interval Estimation

 

  1. Define relative efficiency.

 

ANS:

If there are two unbiased estimators of a parameter, the one whose variance is smaller is relatively efficient.

 

NAT:   Analytic; Interval Estimation

 

  1. Draw the sampling distribution of two unbiased estimators for m, one of which is relatively efficient.

 

ANS:

 

NAT:   Analytic; Interval Estimation

 

  1. Explain briefly why interval estimators are preferred to point estimators.

 

ANS:

An interval estimator incorporates the effects of sample size, but point estimators don’t have the capacity to do this.

 

NAT:   Analytic; Interval Estimation

 

  1. A random sample of 10 university students was surveyed to help estimate the average amount of time students spent per week on their computers. The student hours spent using a personal computer over a randomly selected week were 13, 14, 5, 6, 8, 10, 7, 12, 15, 3.

 

a. Find an unbiased estimator of the average time per week for all university students.
b. Find an unbiased estimator of the variance.
c. Find a consistent estimator of the average time per week for all university students.

 

 

ANS:

 

a. An unbiased estimator of the population mean is the sample mean, 9.30 hours.
b. An unbiased estimator of the population variance is the sample variance, 16.9 hours.
c. A consistent estimator of the population mean is the sample mean, 9.30 hours.

 

 

NAT:   Analytic; Interval Estimation

 

NARRBEGIN: Socialist Voters

Socialist Party Voters

 

A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that. In a test of hypothesis, H0: p = 0.05 vs. H1: p < 0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40.

NARREND

 

 

  1. {Socialist Voters Narrative} Test the hypotheses at the 5% significance level.

 

ANS:

Rejection region: z < –z0.05 = -1.645

Test Statistic: z = -1.451

Conclusion: Don’t reject H0. Cannot conclude that the proportion of Socialist voters in the country is less than 0.05.

 

NAT:   Analytic; Hypothesis Testing

 

  1. {Socialist Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses.

 

ANS:

p-value = 0.0735.

Since p-value = 0.0735 > a = 0.05, don’t reject H0.

 

NAT:   Analytic; Hypothesis Testing

 

  1. {Socialist Voters Narrative} Construct a 95% confidence interval estimate of the population proportion and explain how to use it to test the hypotheses.

 

ANS:

. Thus, LCL = 0.028, and UCL = 0.052.

Since the hypothesized value p0 = 0.05 is included in the 95% confidence interval, we fail to reject H0 at a = 0.05.

 

NAT:   Analytic; Hypothesis Testing

 

  1. As a manufacturer of guitars, a major corporation wants to estimate the proportion of guitar players who are right-handed. How many golfers must be surveyed if they want to be within 0.02, with a 95% confidence?

 

a. Assume that there is no prior information that could be used as an estimate of .
b. Assume that the manufacturer has an estimate of  found from a previous study, which suggests that 75% of guitar players are right-handed.

 

 

ANS:

 

a. n = 2401
b. n = 1801

 

 

NAT:   Analytic; Hypothesis Testing

 

NARRBEGIN: Physicians

Physicians

 

A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year.

NARREND

 

 

  1. {Physicians Narrative} Can we conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24?

 

ANS:

H0: p = 0.24, H1: p < 0.24

Rejection region: z < –z0.01 = -2.33

Test statistic: z = -1.99

Conclusion: Don’t reject H0. No, we can’t conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24.

 

NAT:   Analytic; Hypothesis Testing

 

  1. {Physicians Narrative} Compute the p-value and explain how to use it to test the hypotheses.

 

ANS:

p-value = 0.0233.

Since p-value = 0.0233 > a = 0.01, don’t reject H0.

 

NAT:   Analytic; Hypothesis Testing

 

  1. {Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year, and explain how to use it to test the hypotheses.

 

ANS:

. Thus, LCL = 0.11, and UCL = 0.25.

Since the hypothesized value p0 = 0.24 is included in the 99% confidence interval, we fail to reject H0 at a = 0.01.

 

NAT:   Analytic; Hypothesis Testing

 

  1. An engineer for an electric fencing company  is interested in the mean length of wires being cut automatically by machine. The desired length of the wires is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. Suppose the engineer decided to estimate the mean length to within 0.025 with 99% confidence. What sample size would be needed?

 

ANS:

n = 240 (using z = 2.58)

 

NAT:   Analytic; Interval Estimation

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