# Understanding Statistics In the Behavioral Sciences 9th Edition by Robert R. Pagano -Test Bank

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###### Understanding Statistics In the Behavioral Sciences 9th Edition by Robert R. Pagano -Test Bank

Chapter 2—Basic Mathematical and Measurement Concepts

MULTIPLE CHOICE

1. Given the following subjects and scores, which symbol would be used to represent the score of 3?

 Subject 1 2 3 4 5 Score 12 21 8 3 30

 a. X8 b. X4 c. X3 d. X2

ANS:  B                    PTS:   1                    MSC:  WWW

1. We have collected the following data:

X1 = 6, X2 = 2, X3 = 4, X4 = 1, X5 = 3

For these data,  is equal to ____.

 a. 16 b. 10 c. 7 d. 13

ANS:  D                    PTS:   1                    MSC:  WWW

1. Reaction time in seconds is an example of a(n) ____ scale.
 a. ratio b. ordinal c. interval d. nominal

ANS:  A                    PTS:   1

1. After performing several clever calculations on your calculator, the display shows the answer 53.655001. What is the appropriate value rounded to two decimal places?
 a. 53.65 b. 53.66 c. 53.64 d. 53.6

ANS:  B                    PTS:   1

1. Consider the following points on a scale:

If the scale upon which A, B, C, and D are arranged is a nominal scale, we can say ____.

 a. B = 2A b. B – A = D – C c. both a and b d. neither a nor b

ANS:  D                    PTS:   1

1. When rounded to two decimal places, the number 3.175000 becomes ____.
 a. 3.17 b. 3.2 c. 3.18 d. 3.1

ANS:  C                    PTS:   1                    MSC:  WWW

Exhibit 2-1

Given the following data:

X1 = 1, X2 = 4, X3 = 5, X4 = 8, X5 = 10

1. Refer to Exhibit 2-1. Evaluate S X.
 a. 1 b. 18 c. 27 d. 28

ANS:  D                    PTS:   1

1. Refer to Exhibit 2-1. Evaluate S X2.
 a. 56 b. 784 c. 206 d. 28

ANS:  C                    PTS:   1

1. Refer to Exhibit 2-1. Evaluate (S X)2.
 a. 56 b. 784 c. 206 d. 28

ANS:  B                    PTS:   1

1. Refer to Exhibit 2-1. Evaluate .
 a. 17 b. 27 c. 28 d. 23

ANS:  A                    PTS:   1

1. Refer to Exhibit 2-1. Evaluate .
 a. 53 b. 47 c. 48 d. 32

ANS:  D                    PTS:   1

1. Refer to Exhibit 2-1. Evaluate .
 a. 47 b. 53 c. 48 d. 32

ANS:  A                    PTS:   1

1. A discrete scale of measurement ____.
 a. is the same as a continuous scale b. provides exact measurements c. necessarily uses whole numbers d. b and c

ANS:  B                    PTS:   1

1. Consider the following points on a scale:

If the scale upon which A, B, C, and D are arranged is an interval scale, we can say ____.

 a. B = 2A b. B – A = D – C c. both a and b d. neither a nor b

ANS:  B                    PTS:   1                    MSC:  WWW

1. The number 83.476499 rounded to three decimal places is ____.
 a. 83.477 b. 83.48 c. 83.476 d. 83.47

ANS:  C                    PTS:   1

1. The number 99.44650 rounded to two decimal places is ____.
 a. 99.45 b. 99.46 c. 99.44 d. 99.4

ANS:  A                    PTS:   1

1. “Brand of soft drink” is measured on a(n) ____.
 a. nominal scale b. ordinal scale c. interval scale d. ratio scale

ANS:  A                    PTS:   1

1. At the annual sailing regatta, prizes are awarded for 1st, 2nd, 3rd, 4th, and 5th place. These “places” comprise a(n) ____.
 a. nominal scale b. ordinal scale c. interval scale d. ratio scale

ANS:  B                    PTS:   1

1. Which of the following numbers is rounded incorrectly to two decimal places?
 a. 10.47634 ® 10.48 b. 15.36485 ® 15.36 c. 21.47500 ® 21.47 d. 8.24501 ®   8.25 e. 6.66500 ®   6.66

ANS:  C                    PTS:   1

1. Consider the following points on a scale:

If the scale upon which points A, B, C, and D are shown is an ordinal scale, we can meaningfully say ____.

 a. B – A < D – C b. B < C/2 c. B = 2A d. C > B

ANS:  D                    PTS:   1

1. A continuous scale of measurement is different than a discrete scale in that a continuous scale ____.
 a. is an interval scale, not a ratio scale b. never provides exact measurements c. can take an infinite number of intermediate possible values d. never uses decimal numbers e. b and c

ANS:  E                    PTS:   1

1. Sex of children is an example of a(n) ____ scale.
 a. ratio b. nominal c. ordinal d. interval

ANS:  B                    PTS:   1

1. Which of the following variables has been labeled with an incorrect measuring scale?
 a. the number of students in a psychology class – ratio b. ranking in a beauty contest – ordinal c. finishing order in a poetry contest – ordinal d. self-rating of anxiety level by students in a statistics class – ratio

ANS:  D                    PTS:   1

1. A nutritionist uses a scale that measures weight to the nearest 0.01 grams. A slice of cheese weighs 0.35 grams on the scale. The variable being measured is a ____.
 a. discrete variable b. constant c. continuous variable d. random variable

ANS:  C                    PTS:   1

1. A nutritionist uses a scale that measures weight to the nearest 0.01 grams. A slice of cheese weighs 0.35 grams on the scale. The true weight of the cheese ____.
 a. is 0.35 grams b. may be anywhere in the range 0.345-0.355 grams c. may be anywhere in the range 0.34-0.35 grams d. may be anywhere in the range 0.34-0.36 grams

ANS:  B                    PTS:   1

1. In a 10-mile cross-country race, all runners are randomly assigned an identification number. These numbers represent a(n) ____.
 a. nominal scale b. ratio scale c. interval scale d. ordinal scale

ANS:  A                    PTS:   1

1. In a 10-mile cross-country race, a comparison of each runner’s finishing time would represent a(n) ____.
 a. nominal scale b. ratio scale c. interval scale d. ordinal scale

ANS:  B                    PTS:   1

1. The sum of a distribution of 40 scores is 150. If we add a constant of 5 to each score, the resulting sum will be ____.
 a. 158 b. 350 c. 150 d. 195

ANS:  B                    PTS:   1

Exhibit 2-2

Given the following set of numbers:

X1 = 2, X2 = 4, X3 = 6, X4 = 10

1. Refer to Exhibit 2-2. What is the value for S X?
 a. 12 b. 156 c. 480 d. 22

ANS:  D                    PTS:   1

1. Refer to Exhibit 2-2. What is the value of S X2?
 a. 156 b. 22 c. 480 d. 37

ANS:  A                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 2-2. What is the value of X42?
 a. 4 b. 6 c. 100 d. 10

ANS:  C                    PTS:   1

1. Refer to Exhibit 2-2. What is the value of (S X)2?
 a. 480 b. 484 c. 156 d. 44

ANS:  B                    PTS:   1

1. Refer to Exhibit 2-2. What is the value of N?
 a. 2 b. 4 c. 6 d. 10

ANS:  B                    PTS:   1

1. Refer to Exhibit 2-2. What is the value of (S X)/N?
 a. 5 b. 4 c. 6 d. 5.5

ANS:  D                    PTS:   1

1. Classifying subjects on the basis of sex is an example of using what kind of scale?
 a. nominal b. ordinal c. interval d. ratio e. bathroom

ANS:  A                    PTS:   1                    MSC:  WWW

1. Number of bar presses is an example of a(n) ____ variable.
 a. discrete b. continuous c. nominal d. ordinal

ANS:  A                    PTS:   1

1. Using an ordinal scale to assess leadership, which of the following statements is appropriate?
 a. A has twice as much leadership ability as B b. X has no leadership ability c. Y has the most leadership ability d. all of the above

ANS:  C                    PTS:   1

1. The number of legs on a centipede is an example of a(n) ____ scale.
 a. nominal b. ordinal c. ratio d. continuous

ANS:  C                    PTS:   1

1. What are the real limits of the observation of 6.1 seconds (measured to the nearest second)?
 a. 6.05–6.15 b. 5.5–6.5 c. 6.0–6.2 d. 6.00–6.20

ANS:  A                    PTS:   1                    MSC:  WWW

1. What is 17.295 rounded to one decimal place?
 a. 17.1 b. 17 c. 17.2 d. 17

ANS:  D                    PTS:   1

1. What is the value of 0.05 rounded to one decimal place?
 a. 0 b. 0.1 c. 0.2 d. 0.5

ANS:  A                    PTS:   1

1. The symbol “S” means:
 a. add the scores b. summarize the data c. square the value d. multiply the scores

ANS:  A                    PTS:   1

1. A therapist measures the difference between two clients. If the therapist can say that Rebecca’s score is higher than Sarah’s, but can’t specify how much higher, the measuring scale used must have been a(n) ____ scale.
 a. nominal b. ordinal c. interval d. ratio

ANS:  B                    PTS:   1                    MSC:  WWW

1. An individual is measuring various objects. If the measurements made are to determine into which of six categories each object belongs, the measuring scale used must have been a(n)____ scale.
 a. nominal b. ordinal c. interval d. ratio

ANS:  A                    PTS:   1                    MSC:  WWW

1. If an investigator determines that Carlo’s score is five times as large as the score of Juan, the measuring scale used must have been a(n) ____ scale.
 a. nominal b. ordinal c. interval d. ratio

ANS:  D                    PTS:   1                    MSC:  WWW

The following problem(s) are for your own use in evaluating your skills at elementary algebra. If you do not get all the problem(s) correct you should probably review your algebra.

1. Where 3X = 9, what is the value of X?
 a. 3 b. 6 c. 9 d. 12

ANS:  A                    PTS:   1

1. For X + Y = Z, X equals ____.
 a. Y + Z b. Z – Y c. Z/Y d. Y/Z

ANS:  B                    PTS:   1

1. 1/X + 2/X equals ____.
 a. 2/X b. 3/2X c. 3/X d. 2/X2

ANS:  C                    PTS:   1

1. What is (4 – 2)(3×4)/(6/3)?
 a. 24 b. 1.3 c. 12 d. 6

ANS:  C                    PTS:   1

1. 6 + 4´3 – 1 simplified is ____.
 a. 29 b. 48 c. 71 d. 17

ANS:  D                    PTS:   1

1. X = Y/Z can be expressed as ____.
 a. Y = (Z)(X) b. X = Z/Y c. Y = X/Z d. Z = X + Y

ANS:  A                    PTS:   1

1. 24 equals ____.
 a. 4 b. 32 c. 8 d. 16

ANS:  D                    PTS:   1

1.  equals ____.
 a. ±3 b. ±81 c. ±9 d. ±27

ANS:  C                    PTS:   1

1. X(Z + Y) equals ____.
 a. XZ + Y b. ZX + YX c. (X)(Y)(Z) d. (Z + Y)/X

ANS:  B                    PTS:   1

1. 1/2 + 1/4 equals ____.
 a. 1/6 b. 1/8 c. 2/8 d. 3/4

ANS:  D                    PTS:   1

1. X6/X2 equals ____.
 a. X8 b. X4 c. X2 d. X3

ANS:  B                    PTS:   1

TRUE/FALSE

1. When doing summation, the number above the summation sign indicates the term ending the summation and the number below indicates the beginning term.

ANS:  T                    PTS:   1                    MSC:  WWW

1. S X2 and (S X)2 generally yield the same answer.

ANS:  F                    PTS:   1                    MSC:  WWW

1. With nominal scales there is a numerical relationship between the units of the scale.

ANS:  F                    PTS:   1

1. If IQ was measured on a ratio scale, and John had an IQ of 40 and Fred an IQ of 80, it would be correct to say that Fred was twice as intelligent as John.

ANS:  T                    PTS:   1

1. An ordinal scale possesses the attributes of magnitude and equal interval.

ANS:  F                    PTS:   1

1. Most scales used for measuring psychological variables are either ratio or interval.

ANS:  F                    PTS:   1

1. Measurement is always approximate with a continuous variable.

ANS:  T                    PTS:   1                    MSC:  WWW

1. It is standard practice to carry all intermediate calculations to four more decimal places than will be reported in the final answer.

ANS:  F                    PTS:   1

1. In rounding, if the remainder beyond the last digit is greater than 1/2, add one to the last digit. If the remainder is less than 1/2, leave the last digit as it is.

ANS:  T                    PTS:   1

1. It is legitimate to do ratios with interval scaling.

ANS:  F                    PTS:   1

1. The number of students in a class is an example of a continuous variable.

ANS:  F                    PTS:   1

1. The real limits of a discrete variable are those values that are above and below the recorded value by one half of the smallest measuring unit of the scale.

ANS:  F                    PTS:   1

1. When rounding, if the decimal remainder is equal to 1/2 and the last digit of the answer is even, add 1 to the last digit of the answer.

ANS:  F                    PTS:   1

1. A fundamental property of a nominal scale is equivalence.

ANS:  T                    PTS:   1

1. An interval scale is like a ratio scale, except that the interval scale doesn’t possess an absolute zero point.

ANS:  T                    PTS:   1

1. A discrete variable requires nominal or interval scaling.

ANS:  T                    PTS:   1                    MSC:  WWW

1. Classifying students into whether they are good, fair, or poor speakers is an example of ordinal scaling.

ANS:  T                    PTS:   1

1. Determining the number of students in each section of introductory psychology involves the use of a ratio scale.

ANS:  T                    PTS:   1                    MSC:  WWW

1. In a race, Sam came in first and Fred second. Determining the difference in time to complete the race between Sam and Fred involves an ordinal scale

ANS:  F                    PTS:   1

1. If the remainder of a number = 1/2, we always round the last digit up.

ANS:  F                    PTS:   1

DEFINITIONS

1. Define continuous variable.

ANS:

PTS:   1                    MSC:  WWW

1. Define discrete variable.

ANS:

PTS:   1

1. Define interval scale.

ANS:

PTS:   1

1. Define nominal scale.

ANS:

PTS:   1

1. Define ratio scale.

ANS:

PTS:   1                    MSC:  WWW

1. Define real limits of a continuous variable.

ANS:

PTS:   1

1. How does an interval scale differ from an ordinal scale?

ANS:

PTS:   1

1. Give two differences between continuous and discrete scales.

ANS:

PTS:   1

1. What are the four types of scales and what mathematical operations can be done with each?

ANS:

PTS:   1

1. Prove algebraically that .

ANS:

PTS:   1

1. What is a discrete variable? Give an example.

ANS:

PTS:   1

1. Student A claims that because his IQ is twice that of Student B, he is twice as smart as Student B. Is student A correct? Explain.

ANS:

PTS:   1

1. What is meant by “the real limits of a continuous variable.”

ANS:

PTS:   1                    MSC:  WWW

1. The faculty of a psychology department are trying to decide between three candidates for a single faculty position. The department chairperson suggests that to decide, each faculty person should rank order the candidates from 1 to 3, and the ranks would then be averaged. The candidate with the highest average would be offered the position. Mathematically, what is wrong with that proposal?

ANS:

PTS:   1                    MSC:  WWW

Chapter 8—Random Sampling and Probability

MULTIPLE CHOICE

1. If events A and B are independent, then p(A and B) = ____.
 a. p(A) + p(B) – p(A and B) b. p(A)p(B) c. p(A or B) d. 0

ANS:  B                    PTS:   1

1. If A and B are mutually exclusive and exhaustive, then p(A and B) = ____.
 a. 1 b. 0 c. p(A) + p(B) d. p(A) + p(B) – p(A and B)

ANS:  B                    PTS:   1

1. If the odds in favor of an event occurring are 9 to 1, the probability of the event occurring is ____.
 a. 9 b. 1/9 c. 9/10 d. 8/9

ANS:  C                    PTS:   1

1. Probabilities vary between ____.
 a. 0 and 2 b. 0 and 100 c. -1 and 0 d. 0 and 1

ANS:  D                    PTS:   1

1. The Addition Rule states ____.
 a. p(A or B) = p(A) + p(B) – p(A and B) b. p(A and B) = p(A)p(B|A) c. P + Q = 1 d. p(A)p(B|A) = p(A)p(B)

ANS:  A                    PTS:   1

1. A sample is random if ____.
 a. each possible sample of a given size has an equal chance of being selected b. all members of the population have an equal chance of being selected into the sample c. all members of the sample have an equal chance of being selected d. a, or a and b e. a and c

ANS:  D                    PTS:   1

1. The Multiplication Rule states ____.
 a. p(A or B) = p(A) + p(B) – p(A and B) b. p(A or B) = p(A) + p(B) c. p(A and B) = p(A)p(B|A) d. p(A and B) = p(A) + p(B)

ANS:  C                    PTS:   1

1. A priori probability refers to ____.
 a. a probability value deduced from reason alone b. the highest priority probability c. a probability value determined after collecting data d. none of the above

ANS:  A                    PTS:   1

1. A posteriori probability refers to ____.
 a. a probability value deduced from reason alone b. low priority probability c. a probability value determined after collecting data d. none of the above

ANS:  C                    PTS:   1

1. Two events are mutually exclusive if ____.
 a. they are independent b. they both cannot occur together c. the occurrence of one slightly alters the probability of occurrence of the other d. the probability of their joint occurrence equals one

ANS:  B                    PTS:   1

1. A set of events is exhaustive if ____.
 a. the sum of their probabilities equals one b. the set includes all of the possible events c. they are mutually exclusive d. they are independent

ANS:  B                    PTS:   1

1. Two events are independent if ____.
 a. the occurrence of one has no effect on the probability of occurrence of the other b. the occurrence of one precludes the occurrence of the other c. the occurrence of one substantially alters the probability of occurrence of the other d. the sum of their probabilities equals one e. a and d

ANS:  A                    PTS:   1

1. Suppose you are going to randomly order individuals A, B, C, D, E and F. The probability the order will begin A B _ _ _ _ is ____.
 a. 1 b. 0.033 c. 0.027 d. 0

ANS:  B                    PTS:   1

1. A famous hypnotist performs in Meany Hall before a crowd of 350 students and 180 non-students. The hypnotist knows from previous experience that one-half of the students and two-thirds of the non-students are hypnotizable. What is the probability that a randomly chosen person from the audience will be hypnotizable or will be a non-student?
 a. 0.33 b. 0.34 c. 0.869 d. 0.67

ANS:  D                    PTS:   1

1. Captain Kirk and Mr. Spock are engaged in a 3-D backgammon playoff, a game employing 6 dice. Kirk asks Spock the probability of rolling the dice and observing 6 sixes. Assume the dice are not biased. Spock’s correct a priori reply is ____.
 a. “Insufficient data, Captain.” b. “One-sixth to the sixth power, Sir.” Translation: (1/6)6 c. “One-thirtysixth, Sir.” d. “One-thirtysix to the sixth power, Sir.” (1/36)6 e. “The probability is equal to (1/6) ´ (1/5) ´ (1/4) ´ (1/3) ´ (1/2) ´ (1/1), Sir.” (1/720)

ANS:  B                    PTS:   1

Exhibit 8-1

A “hungry” undergraduate student was looking for a way of making some extra money. The student turned to a life of vice – gambling. To be a good gambler, he needed to know the probability of certain events. Help him out by answering the following questions.

1. Refer to Exhibit 8-1. The probability of drawing 3 aces in a row without replacement from a deck of 52 ordinary playing cards is ____.
 a. 0.00018 b. 0.00046 c. 0.00017 d. 0.00045

ANS:  A                    PTS:   1

1. Refer to Exhibit 8-1. The probability of drawing a face card (king, queen or jack) of any suit from a deck of 52 ordinary playing cards in one draw is ____.
 a. 0.02 b. 0.231 c. 0.077 d. 0.019

ANS:  B                    PTS:   1

1. Refer to Exhibit 8-1. The probability of drawing an ace, a king and a queen of any suit in that order is ____. Sampling is without replacement from a deck of 52 ordinary playing cards.
 a. 0.00045 b. 0.00046 c. 0.00048 d. 0.00018

ANS:  C                    PTS:   1

1. Refer to Exhibit 8-1. The probability of rolling “boxcars” (two sixes) with one roll of a pair of fair dice is ____.
 a. 0.167 b. 0.333 c. 0.033 d. 0.028

ANS:  D                    PTS:   1

1. A royal flush in poker is when you end up with the ace, king, queen, jack, and 10 of the same suit. It’s the most rare event in poker. If you are playing with a well-shuffled, legitimate deck of 52 cards, what is the probability that if you are dealt 5 cards, you will have a royal flush? Assume randomness.
 a. 3.2e-09 b. 1.3e-08 c. 1.5e-06 d. 4e-07

ANS:  B                    PTS:   1

Exhibit 8-2

Let’s assume you are having a party and have stocked your refrigerator with beverages. You have 12 bottles of Coors beer, 24 bottles of Rainier beer, 24 bottles of Schlitz light beer, 12 bottles of Hamms beer, 2 bottles of Heineken dark beer and 6 bottles of Pepsi soda. You go to the refrigerator to get beverages for your friends. In answering the following questions assume you are randomly sampling without replacement.

1. Refer to Exhibit 8-2. What is the probability the first beverage you get is a beer?
 a. 0.925 b. 0.9 c. 0.9487 d. 0.775

ANS:  A                    PTS:   1

1. Refer to Exhibit 8-2. What is the probability the first bottle selected is a Coors beer?
 a. 0.075 b. 0.15 c. 0.3 d. 0.1622

ANS:  B                    PTS:   1

1. Refer to Exhibit 8-2. What is the probability your first three bottles selected are Pepsi’s?
 a. 0.00044 b. 0.00024 c. 0.1875 d. 0.225

ANS:  B                    PTS:   1

1. Refer to Exhibit 8-2. What is the probability the first four bottles you select will be a Coors, a Schlitz, a Rainier, and a Coors in that order?
 a. 0.002 b. 0.0022 c. 0.8875 d. 0.0019

ANS:  A                    PTS:   1

Exhibit 8-3

Assume you are rolling two fair dice once.

1. Refer to Exhibit 8-3. The probability of obtaining a sum of 5 equals ____.
 a. 0.3333 b. 0.0228 c. 0.1111 d. 0.0556

ANS:  C                    PTS:   1

1. Refer to Exhibit 8-3. The probability of obtaining a sum of 2 or 12 equals ____.
 a. 0.0228 b. 0.3333 c. 0.0833 d. 0.0556

ANS:  D                    PTS:   1

1. Refer to Exhibit 8-3. The probability of obtaining at least one 3 or one 4 equals ____.
 a. 0.3333 b. 0.5556 c. 0.1111 d. 0.0833

ANS:  B                    PTS:   1

1. Which of the following are examples of mutually exclusive events?
 a. rain and a cloudless sky b. snow and a temperature of 10° Celsius c. walking and running at the same time d. all of the above e. a and c

ANS:  D                    PTS:   1                    MSC:  WWW

Exhibit 8-4

A certain university maintains a colony of male mice for research purposes. The ages of the mice are normally distributed with a mean of 60 days and a standard deviation of 5.2. Assume you randomly sample one mouse from the colony.

1. Refer to Exhibit 8-4. The probability his age will be less than 45 days is ____.
 a. 0.998 b. 0.498 c. 0.002 d. 0.0019

ANS:  C                    PTS:   1

1. Refer to Exhibit 8-4. The probability his age will be between 55 and 70 days is ____.
 a. 0.8041 b. 0.498 c. 0.8066 d. 0.1959

ANS:  A                    PTS:   1

1. Refer to Exhibit 8-4. The probability his age will be greater than 68 is ____.
 a. 0.4382 b. 0.0618 c. 0.9382 d. 0.063

ANS:  B                    PTS:   1

1. If a town of 7000 people has 4000 females in it, then the probability of randomly selecting 6 females in six draws (with replacement) equals ____.
 a. 0.0348 b. 0.0571 c. 0.5714 d. 0.3429

ANS:  A                    PTS:   1                    MSC:  WWW

1. If a stranger gives you a coin and you toss it 1,000,000 times and it lands on heads 600,000 times, what is p(Heads) for that coin?
 a. 0.5 b. 0.6 c. 0.4 d. 0

ANS:  B                    PTS:   1

1. The probability of randomly selecting a face card (K, Q, or J) or a spade in one draw equals ____.
 a. 0.0192 b. 0.0577 c. 0.4808 d. 0.4231

ANS:  D                    PTS:   1                    MSC:  WWW

1. The probability of drawing an ace followed by a king (without replacement) equals ____.
 a. 0.0044 b. 0.006 c. 0.0045 d. 0.0965

ANS:  B                    PTS:   1

1. The probability of throwing two ones with a pair of dice equals ____.
 a. 0.36 b. 0.1667 c. 0.0278 d. 0.3333

ANS:  C                    PTS:   1

1. If p(A or B) = p(A) + p(B) then A and B must be ____.
 a. dependent b. mutually exclusive c. overlapping d. continuous

ANS:  B                    PTS:   1

1. If P + Q = 1.00 then P and Q must be ____.
 a. mutually exclusive b. exhaustive c. random d. a and b

ANS:  D                    PTS:   1                    MSC:  WWW

1. If m = 35.2 and s = 10, then p(X) for X £ 39 equals ____. Assume random sampling.
 a. 0.352 b. 0.62 c. 0.148 d. 0.648

ANS:  D                    PTS:   1                    MSC:  WWW

1. If p(A and B) = 0, then A and B must be ____.
 a. independent b. mutually exclusive c. exhaustive d. unbiased

ANS:  B                    PTS:   1                    MSC:  WWW

1. If p(A)p(B|A) = p(A)p(B), then A and B must be ____.
 a. independent b. mutually exclusive c. random d. exhaustive

ANS:  A                    PTS:   1

1. If p(A and B) = p(A)p(B|A) ¹ p(A)p(B), then A and B are ____.
 a. mutually exclusive b. random c. independent d. dependent

ANS:  D                    PTS:   1                    MSC:  WWW

1. If p(A) = 0.6 and p(B) = 0.5, then p(B|A) equals ____.
 a. 0.8333 b. 0.3000 c. 0.5000 d. cannot be determined from the information given

ANS:  D                    PTS:   1

1. If m = 400 and s = 100 the probability of selecting at random a score less than or equal to 370 equals ____.
 a. 0.1179 b. 0.6179 c. 0.3821 d. 0.8821

ANS:  C                    PTS:   1                    MSC:  WWW

1. If you have 15 red socks (individual, not pairs), 24 green socks, 17 blue socks, and 100 black socks, what is the probability you will reach in the drawer and randomly select a pair of green socks? (Assume sampling without replacement.)
 a. 0.3022 b. 0.3077 c. 0.0228 d. 0.0227

ANS:  C                    PTS:   1

1. If the probability of drawing a member of a population is not equal for all members, then the sample is said to be ____.
 a. random b. independent c. exhaustive d. biased

ANS:  D                    PTS:   1                    MSC:  WWW

1. The probability of rolling an even number or a one on a throw of a single die equals ____.
 a. 0.6667 b. 0.5 c. 0.0834 d. 0.3333

ANS:  A                    PTS:   1

1. If events are mutually exclusive they cannot be ____.
 a. independent b. exhaustive c. related d. all of the above

ANS:  A                    PTS:   1

1. The probability of correctly guessing a two digit number is ____.
 a. 0.1 b. 0.01 c. 0.2 d. 0.5

ANS:  B                    PTS:   1                    MSC:  WWW

1. When events A and B are mutually exclusive but not exhaustive, p(A or B) equals ____.
 a. 0.50 b. 0.00 c. 1.00 d. cannot be determined from the information given

ANS:  D                    PTS:   1

1. The probability of correctly calling 4 tosses of an unbiased coin in a row equals ____.
 a. 0.0625 b. 0.5 c. 0.125 d. 0.2658

ANS:  A                    PTS:   1

TRUE/FALSE

1. A random sample results when each possible sample of a given size has an equal chance of being selected.

ANS:  T                    PTS:   1                    MSC:  WWW

1. When a sampled score is put back in the population before selecting the next score, this process is called sampling without replacement.

ANS:  F                    PTS:   1

1. A priori and a posteriori probability have the same meaning.

ANS:  F                    PTS:   1                    MSC:  WWW

1. Probability values range from 0 to 1.

ANS:  T                    PTS:   1

1. The Addition Rule concerns one of several possible events.

ANS:  T                    PTS:   1

1. The Multiplication Rule concerns the joint or successive occurrence of several events.

ANS:  T                    PTS:   1                    MSC:  WWW

1. If two events are mutually exclusive, they must be dependent.

ANS:  T                    PTS:   1                    MSC:  WWW

1. If a set of events is exhaustive, they only constitute a part of the possible events.

ANS:  F                    PTS:   1

1. For all problems, we must use either the Addition Rule or the Multiplication Rule, but not both.

ANS:  F                    PTS:   1

1. When a variable is continuous, p(A) equals the area under the curve corresponding to A divided by the total area under the curve.

ANS:  T                    PTS:   1

1. If two events are mutually exclusive and exhaustive, P + Q = 1.

ANS:  T                    PTS:   1

1. p(B|A) is read probability of B divided by A.

ANS:  F                    PTS:   1

1. If sampling is without replacement, the events are independent.

ANS:  F                    PTS:   1                    MSC:  WWW

1. If an event is certain to occur, its probability of occurrence equals 1.00.

ANS:  T                    PTS:   1

1. If an event is certain not to occur, its probability of occurrence equals 0.00.

ANS:  T                    PTS:   1

DEFINITIONS

1. Define addition rule.

ANS:

PTS:   1

1. Define a posteriori.

ANS:

PTS:   1

1. Define a priori.

ANS:

PTS:   1

1. Define exhaustive set of events.

ANS:

PTS:   1

1. Define independence of two events.

ANS:

PTS:   1                    MSC:  WWW

1. Define multiplication rule.

ANS:

PTS:   1

1. Define mutually exclusive.

ANS:

PTS:   1                    MSC:  WWW

1. Define probability.

ANS:

PTS:   1

1. Define probability of occurrence of A or B.

ANS:

PTS:   1

1. Define probability of occurrence of both A and B.

ANS:

PTS:   1

1. Define random sample.

ANS:

PTS:   1

1. Define sampling with replacement.

ANS:

PTS:   1

1. Define sampling without replacement.

ANS:

PTS:   1

1. Define sampling with replacement and sampling without replacement. Give an example of each.

ANS:

PTS:   1

1. Why is random sampling important?

ANS:

PTS:   1

1. Define the addition and multiplication rules. Give an example of each.

ANS:

PTS:   1

1. What is the definition of probability when the variable is continuous?

ANS:

PTS:   1

1. If a set of events is exhaustive and mutually exclusive, then the sum of the probability of occurrence of each event in the set equals one. Is this true? Illustrate your answer by giving an example.

ANS:

PTS:   1

1. The process of random sampling guarantees that the sample selected will be representative of the population. Is this statement true? Discuss.

ANS:

PTS:   1                    MSC:  WWW

1. Assume you are sampling one score from a rectangular distribution of population scores having a mean = 40 and a standard deviation = 15. You want to determine the probability of getting a score ³48. You compute the z transformation of 48 and look up the area corresponding to the z score in Table A (column C) of your textbook. You conclude that this area gives the desired probability. Is this conclusion correct? Discuss.

ANS:

PTS:   1                    MSC:  WWW

Chapter 16—Introduction to Two-Way Analysis of Variance

MULTIPLE CHOICE

1. A significant interaction effect occurs when ____.
 a. there are no main effects b. variable A has a main effect and variable B does not c. the combined effects of variables A and B yield an unexpected effect d. none of the above

ANS:  C                    PTS:   1

1. The null hypothesis for the two-way ANOVA asserts that ____.
 a. the within-cells variance estimate is an estimate of s2 b. c. d. e. all of the above f. b, c and d

ANS:  F                    PTS:   1

1. Which of the following increase(s) as the effect of the A variable increases?
 a. sR2 b. sC2 c. sW2 d. sRC2

ANS:  A                    PTS:   1

1. Which of the following increase(s) as the effect of the B variable increases?
 a. sR2 b. sC2 c. sW2 d. sRC2

ANS:  B                    PTS:   1

1. Which of the following increase(s) as the interaction effect increases?
 a. sR2 b. sC2 c. sW2 d. sRC2

ANS:  D                    PTS:   1

1. If the null hypothesis is correct, which of the following is (are) an estimate of s2?
 a. sR2 b. sC2 c. sW2 d. sRC2 e. all of the above

ANS:  E                    PTS:   1

1. If there are no main effects, then ____.
 a. sC2/sW2 is less than Fcrit b. sR2/sW2 is less than Fcrit c. sRC2/sW2 is less than Fcrit d. a and b e. b and c

ANS:  D                    PTS:   1

1. If the A variable has a real effect, ____.
 a. sC2/sW2 must equal or exceed Fcrit b. sR2/sW2 must equal or exceed Fcrit c. it is possible that sC2/sW2 is less than Fcrit d. it is possible that sR2/sW2 is less than Fcrit

ANS:  B                    PTS:   1

1. A main effect for variable A means that ____.
 a. the effect of variable A is the same over all levels of variable B b. the effect of variable A is significant when averaged over all levels of variable B c. the effect of variable A is not the same over all levels of variable B d. variable A has a greater effect than variable B

ANS:  B                    PTS:   1

1. The two-way analysis of variance ____.
 a. assesses the effects of two independent variables in one experiment b. allows an assessment of the interaction between two independent variables c. results in calculation of three F ratio’s d. all of the above e. a and b

ANS:  D                    PTS:   1

1. Which of the following are called “main effects” in a two-way analysis of variance?
 a. the effect of Factor A b. the effect of Factor B c. the interaction of Factors A and B d. all of the above e. a and b

ANS:  E                    PTS:   1

1. In a two-way ANOVA, if there is a significant interaction between Factor A and Factor B, which of the following may be true?
 a. the effect of Factor A is not the same at all levels of Factor B b. the effect of Factor B is not the same at all levels of Factor A c. the effects of the two Factors do not differ across levels d. a and/or b e. need more information

ANS:  D                    PTS:   1

1. The row variance estimate sR2 and the column variance estimate sC2 are used to measure ____.
 a. the main effects of the independent variables b. the interaction effects of the independent variables c. a and b d. none of the above

ANS:  A                    PTS:   1

Exhibit 16-1

An investigator collects the following data on variables A and B, using a two-way independent groups design. Use a = .05 in analyzing the data.

 Variable B Variable A (1) (2) (3) (1) 10 12 14 18 17 13 15 17 22 16 15 19 20 25 19 (2) 15 17 19 23 20 18 19 22 27 21 26 30 31 36 29

1. Refer to Exhibit 16-1. Fobt for the A variable equals ____.
 a. 2.66 b. 16.34 c. 29.11 d. 11.23

ANS:  C                    PTS:   1

1. Refer to Exhibit 16-1. Fobt for the B variable equals ____.
 a. 2.66 b. 16.34 c. 29.11 d. 11.23

ANS:  B                    PTS:   1

1. Refer to Exhibit 16-1. Fobt for the interaction equals ____.
 a. 2.66 b. 16.34 c. 29.11 d. 11.23

ANS:  A                    PTS:   1

1. Refer to Exhibit 16-1. Fcrit for the A variable equals ____.
 a. 3.4 b. 7.82 c. 5.81 d. 4.26

ANS:  D                    PTS:   1

1. Refer to Exhibit 16-1. Fcrit for the B variable equals ____.
 a. 3.4 b. 7.82 c. 5.81 d. 4.26

ANS:  A                    PTS:   1

1. Refer to Exhibit 16-1. Fcrit for the interaction equals ____.
 a. 3.4 b. 7.82 c. 5.81 d. 4.26

ANS:  A                    PTS:   1

1. Refer to Exhibit 16-1. The conclusion regarding the A variable is ____.
 a. retain H0; chance is a reasonable explanation b. reject H0; there is a significant main effect for variable A c. accept H0; variable A has no real effect d. reject H0; chance is a reasonable explanation

ANS:  B                    PTS:   1

1. Refer to Exhibit 16-1. The conclusion regarding the B variable is ____.
 a. reject H0; variable B has no effect b. retain H0; chance is a reasonable explanation c. reject H0; there is a significant main effect for variable B d. accept H0; chance is a reasonable explanation

ANS:  C                    PTS:   1

1. Refer to Exhibit 16-1. The conclusion regarding the interaction is ____.
 a. retain H0; chance is a reasonable explanation b. accept H0; chance is a reasonable explanation c. reject H0; there is a significant interaction between variables A and B d. reject H0; there is no interaction between variables A and B

ANS:  A                    PTS:   1

1. The two-way analysis of variance ____.
 a. assesses the effects of two independent variables in one experiment b. allows an assessment of the interaction between two independent variables c. results in calculation of three F ratios d. all of the above e. a and b

ANS:  D                    PTS:   1

1. Which of the following are called “main effects” in a two-way analysis of variance?
 a. the effect of Factor A b. the effect of Factor B c. the interaction of Factors A and B d. all of the above e. a and b

ANS:  E                    PTS:   1

1. In a two-way ANOVA, if there is a significant interaction between Factor A and Factor B, which of the following may be true?
 a. the effect of Factor A is not the same at all levels of Factor B b. the effect of Factor B is not the same at all levels of Factor A c. the effects of the two Factors do not differ across levels d. a and/or b e. need more information

ANS:  D                    PTS:   1

1. The row variance estimate sR2 and the column variance estimate sC2 are used to measure ____.
 a. the main effects of the independent variables b. the interaction effects of the independent variables c. a and b d. none of the above

ANS:  A                    PTS:   1

Exhibit 16-2

Use the following data, collected from an independent groups design. a = 0.05.

1. Refer to Exhibit 16-2. The value of Fobt for evaluating the row effect is ____.
 a. 0.66 b. 6.23 c. 0.29 d. 5.28

ANS:  A                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The value of Fcrit for evaluating the row effect is ____.
 a. 3.4 b. 7.82 c. 4.26 d. 5.61

ANS:  C                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The conclusion regarding the main effect of variable A is ____.
 a. Retain H0; We cannot conclude variable A has main effect. b. Accept H0; We cannot conclude variable A has main effect. c. Reject H0; Variable A has a significant main effect. d. Reject H0; Variable A has no effect.

ANS:  A                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The value of Fobt for evaluating the column effect is ____.
 a. 0.66 b. 6.23 c. 0.29 d. 5.28

ANS:  B                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The value of Fcrit for evaluating the column effect is ____.
 a. 3.4 b. 7.82 c. 4.26 d. 5.61

ANS:  A                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The conclusion regarding the main effect of variable B is ____.
 a. Retain H0; We cannot conclude variable B has main effect. b. Accept H0; We cannot conclude variable B has main effect. c. Reject H0; Variable B has a significant main effect. d. Reject H0; Variable B has no effect.

ANS:  C                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The value of Fobt for evaluating the row ´ column effect is ____.
 a. 0.66 b. 6.23 c. 0.29 d. 5.28

ANS:  C                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The value of Fcrit for evaluating the row ´ column effect is ____.
 a. 3.4 b. 7.82 c. 4.26 d. 5.61

ANS:  A                    PTS:   1                    MSC:  WWW

1. Refer to Exhibit 16-2. The conclusion regarding the interaction effect of variables A and B is ____.
 a. Retain H0; We cannot conclude there is a significant interaction b. Accept H0; There is no interaction effect between A and B c. Reject H0; There is a significant interaction effect d. Reject H0; There is no interaction effect between A and B

ANS:  A                    PTS:   1                    MSC:  WWW

1. Consider the following graphic results from a 2 ´ 2 factorial experiment. These results show ____.

 a. there are no significant main effects or interaction effects b. there is a significant main effect for factor A, no other significant effects c. there is a significant main effect for factor B, no other significant effects d. there is a significant interaction effect, no other significant effects

ANS:  B                    PTS:   1

1. Consider the following graphic results from a 2 ´ 2 factorial experiment. These results show ____.

 a. there are no significant main effects or interaction effects b. there is a significant main effect for factor A, no other significant effects c. there is a significant main effect for factor B, no other significant effects d. there is a significant interaction effect, no other significant effects

ANS:  C                    PTS:   1

1. Consider the following graphic results from a 2 ´ 2 factorial experiment. These results show ____.

 a. there are no significant main effects or interaction effects b. there is a significant main effect for factor A, no other significant effects c. there is a significant main effect for factor B, no other significant effects d. there is a significant interaction effect, no other significant effects

ANS:  A                    PTS:   1

1. Consider the following graphic results from a 2 ´ 2 factorial experiment. These results show ____.

 a. there are no significant main effects or interaction effects b. there is a significant main effect for factor A, no other significant effects c. there is a significant main effect for factor B, no other significant effects d. there is a significant interaction effect, no other significant effects

ANS:  D                    PTS:   1

1. Consider the following graphic results from a 2 ´ 2 factorial experiment. These results show ____.

 a. there is a significant main effect for factor A, no other significant effects b. there is a significant main effect for factor B, no other significant effects c. there is a significant interaction effect, no other significant effects d. there is a significant main effect for factor A, a significant interaction effect, and no other significant effects e. there is a significant main effect for factor B, a significant interaction effect, and no other significant effects

ANS:  D                    PTS:   1                    MSC:  WWW

1. How many variance estimates are there in a 2 ´ 2 factorial design?
 a. 1 b. 2 c. 3 d. 4

ANS:  D                    PTS:   1

1. Consider the following graphic results from a 2 ´ 2 factorial experiment.

Would you think there is a significant A ´ B interaction?

 a. yes b. no, it is not possible to have a significant interaction in a 2 ´ 2 factorial experiment. c. no, the lines should be parallel for a significant interaction

ANS:  A                    PTS:   1

1. Which of the following are not true statements?
 a. The main effect of factor A is the effect of factor A averaged over the levels of factor B. b. The main effect of factor B is the effect of factor B averaged over the levels of factor A. c. An interaction effect occurs when the effect of one factor is the same for all levels of the other factor. d. All of the above statements are false.

ANS:  C                    PTS:   1

1. In the one-way ANOVA, the within-groups variance estimate is like ____ in two-way ANOVA.
 a. the row variance estimate b. the within-cells variance estimate c. the column variance estimate d. the row ´ column variance estimate

ANS:  B                    PTS:   1

Exhibit 16-3

Refer to the following two-way ANOVA summary table.

 Source SS df s2 Fobt Rows Columns Rows ´ Columns Within cells Total 450.5 116.4 2.3   829.6 2 1 2   29 116.40 1.15 0.11

1. Refer to Exhibit 16-3. What is the value for SS within cells?
 a. 160.4 b. 260.4 c. 250.4 d. 150.4

ANS:  B                    PTS:   1

1. Refer to Exhibit 16-3. What is the value for df within cells?
 a. 2 b. 1 c. 34 d. 24

ANS:  D                    PTS:   1

1. Refer to Exhibit 16-3. What is the value for s2 for Rows?
 a. 225.25 b. 450.5 c. 225.5 d. 9.39

ANS:  A                    PTS:   1

1. Refer to Exhibit 16-3. What is the value for s2 within cells?
 a. 260.4 b. 130.2 c. 10.85 d. 8.98

ANS:  C                    PTS:   1

1. Refer to Exhibit 16-3. What is the value of Fobt for Rows?
 a. 20.76 b. 195.87 c. 1.94 d. 22.53

ANS:  A                    PTS:   1

1. Refer to Exhibit 16-3. What is the value of Fobt for Columns?
 a. 11.64 b. 10.73 c. 4.85 d. 4.01

ANS:  B                    PTS:   1

TRUE/FALSE

1. In two-way ANOVA, SST is partitioned into SSR, SSW, SSC and SSRC.

ANS:  T                    PTS:   1                    MSC:  WWW

1. The within-cells variance estimate measures treatment effects.

ANS:  F                    PTS:   1                    MSC:  WWW

1. The row variance estimate does not change as the effect of the independent variable increases.

ANS:  F                    PTS:   1

1. The column variance estimate increases as the effect of the independent variable increases.

ANS:  T                    PTS:   1

1. A significant interaction effect occurs when the effects of one of the variables is not the same at all levels of the other variable.

ANS:  T                    PTS:   1                    MSC:  WWW

1. Differences among cell means are used to assess the interaction effect.

ANS:  T                    PTS:   1                    MSC:  WWW

1. Differences among row means are used to assess the interaction effect.

ANS:  F                    PTS:   1

1. Differences among column means are used to assess the main effect of one of the variables

ANS:  T                    PTS:   1                    MSC:  WWW

1. SSW for one-way ANOVA and SSW for two-way ANOVA are conceptually similar.

ANS:  T                    PTS:   1

1. SSB for one-way ANOVA is conceptually similar to SSR and SSC for two-way ANOVA.

ANS:  T                    PTS:   1

1. SST = SSR + SSC + SSW

ANS:  F                    PTS:   1

1. It is not possible to have a significant interaction effect unless one of the variables also has a significant main effect.

ANS:  F                    PTS:   1

1. A “mean square” is the same thing as a “variance estimate”.

ANS:  T                    PTS:   1

1. The homogeneity of variance assumption assumes the population scores from which each of the samples are drawn are normally distributed.

ANS:  F                    PTS:   1

1. A two factor experiment yields no more information than two single factor experiments.

ANS:  F                    PTS:   1

1. A factorial experiment is one in which the effect of two or more factors is assessed in one experiment.

ANS:  T                    PTS:   1

1. In a two-way ANOVA, there are three possible main effects and one interaction.

ANS:  F                    PTS:   1

1. In a two-way ANOVA, it is possible to have significant main effects without a significant interaction.

ANS:  T                    PTS:   1

1. If there is an interaction between the variables of “activity level” and “time of day,” this means that activity level does not have the same effect at different times of day.

ANS:  T                    PTS:   1

DEFINITIONS

1. Define column degrees of freedom (dfC).

ANS:

PTS:   1

1. Define column sum of squares (SSC).

ANS:

PTS:   1

1. Define column variance estimate (sC2).

ANS:

PTS:   1

1. Define factorial experiment.

ANS:

PTS:   1

1. Define interaction effect.

ANS:

PTS:   1                    MSC:  WWW

1. Define main effect.

ANS:

PTS:   1                    MSC:  WWW

1. Define row degrees of freedom (dfR).

ANS:

PTS:   1

1. Define row sum of squares (SSR).

ANS:

PTS:   1

1. Define row ´ column degrees of freedom (dfRC).

ANS:

PTS:   1

1. Define row ´ column sum of squares (SSRC).

ANS:

PTS:   1

1. Define row ´ column variance estimate (sRC2).

ANS:

PTS:   1

1. Define row variance estimate (sR2).

ANS:

PTS:   1

1. Define two-way analysis of variance.

ANS:

PTS:   1

1. Define within-cells degrees of freedom (dfW).

ANS:

PTS:   1

1. Define within-cells sum of squares (SSW).

ANS:

PTS:   1

1. Define within-cells variance estimate (sW2).

ANS:

PTS:   1

1. In the two-way ANOVA, what is a main effect? What is an interaction?

ANS:

PTS:   1

1. What is a factorial experiment?

ANS:

PTS:   1

1. What are the advantages of two-way ANOVA as compared to one-way ANOVA?

ANS:

PTS:   1

1. In a two-way ANOVA, how many F values are computed; what are they?

ANS:

PTS:   1

1. In a two-way ANOVA, which variance estimate is a measure of s2 alone (no treatment effects)? Explain.

ANS:

PTS:   1

1. Although not covered in the textbook, generalizing from one-way ANOVA, identify four variables, other than beta, that affect power, and state how power is affected by increases in each. (Remember there are two independent variables, not just one.)

ANS:

PTS:   1                    MSC:  WWW

1. In a two-way ANOVA, the total sum of squares is partitioned into several different sums of squares. What are they?

ANS:

PTS:   1

1. What are the assumptions underlying two-way ANOVA?

ANS:

PTS:   1

1. One of the poorer students in your class insists that there is a direct relationship between sW2 and the size of real effect. Is he correct? Explain.

ANS: