Chapter 5

Question 1

In a sample distribution that conforms to a normal distribution

Select one or more:
a. the probability of scores below z= -2 is greater than the probability of scores above z= +4
b. a larger percentage of scores exist between z-scores of 0 and +1 than between z-scores of +1 and +2
c. a larger percentage of scores exist in quartiles 2 and 3 than in quartiles 1 and 4
d. a z-score of +3 is about at the 5th percentile

Answer 1

a. the probability of scores below z= -2 is greater than the probability of scores above z= +4
b. a larger percentage of scores exist between z-scores of 0 and +1 than between z-scores of +1 and +2

Question 2

A distribution of raw scores has M= 45. A researcher calculates the z-score for X= 55 and obtains z = -2.00. How do you know this is wrong, without doing any calculations?

Select one:
a. none of the other answers is correct
b. s is not given
c. X is above M so z must be positive
d. z scores must lie between -1 and +1

Answer 2

c. X is above M so z must be positive

Question 3

If a positively skewed sample distribution is standardized, what will the shape of the standardized distribution be?

Select one:
a. symmetric
b. positively skewed
c. normal
d. negatively skewed

Answer 3

b. positively skewed

Question 4

What are z-scores good for?

Select one or more:
a. compare location of a score across a sample and a population
b. specify the location of a score in a sample in terms of M and s
c. compare locations of scores across different sample distributions
d. determine the percentile rank of a score in a sample

Answer 4

a. compare location of a score across a sample and a population
b. specify the location of a score in a sample in terms of M and s
c. compare locations of scores across different sample distributions

Question 5

The difference between the z-score for a sample and a population is

Select one:
a. sample z-score represents location; population z-score represents probability
b. there is no difference
c. z-score formula for a sample uses M and s; z-score formula for a population uses μ and σ
d. sample z-score locates a subject in a sample; population z-score locates the sample mean in a population

Answer 5

c. z-score formula for a sample uses M and s; z-score formula for a population uses μ and σ

Question 6

6. A teacher gives a class of people three exams with different maximum possible scores. The table below lists the number of questions (equals maximum number of points possible) on each exam, the class mean (M) and standard deviation (s) of points scored, and the points scored by two particular students (A and B) on all exams. Some values are intentionally left blank.
   The mean % correct score of Student A on all 3 exams is

Answer 6

83.33

Question 7

6. The % correct for Student B on Exam 1 is

Answer 7

70

Question 8

6. Compute the z-score of Student B on Exam 3

Answer 8

1

Question 9

6. The raw score for Student A on Exam 2 is

Answer 9

80

Question 10

6. Which exam was the hardest, and why?

Select one:
a. Exams 2 and 3 are equally harder than Exam 1 because their s is higher
b. Exam 2 is hardest because the mean z-score is lowest
c. Exam 1 is hardest because its mean percent correct was the lowest
d. Exams 1 is hardest because the mean number of points scored was lowest

Answer 10

c. Exam 1 is hardest because its mean percent correct was the lowest

Question 11

6. What is the best inference from the value s=1 for Exam 1?

Select one:
a. The whole class scored on average 1 point from the mean
b. The z-scores of Students A and B can’t be compared
c. The only scores observed on Exam 1 were 20, 21, or 22
d. The distribution of scores for the whole class was symmetric

Answer 11

a. The whole class scored on average 1 point from the mean

Question 12

6. What does Student A’s z-score=9 for Exam 1 mean?

Select one:
a. Student A got the highest score on Exam 1
b. Student A did exceptionally well on Exam 1 compared to all other students
c. None of the other answers is necessarily correct.
d. The distribution of scores for Exam 1 was negatively skewed

Answer 12

c. None of the other answers is necessarily correct.

Question 13

6. The teacher assigns Student A a higher course grade on the basis of a higher average z-score across all three exams than Student B, and Student B protests because his average raw score was higher. What descriptive statistics are lacking for helping the teacher decide?

Select one:
a. How many questions on each exam
b. Student performance in other classes
c. The shapes of the distribution for each exam
d. None of the other answers is correct

Answer 13

c. The shapes of the distribution for each exam

Question 14

7. The following are summary graphs and statistics for the number of IPT questions answered correctly (0 to 9 possible), with the subjects grouped by whether or not they ever owned a dog, in an experiment like the one we conducted in class.

We previously calculated that 3 questions would be answered correctly by chance (guessing).
What is the percentile rank of chance performance in the Non-Dog Owner group?

Answer 14

42

Question 15

7. What is the percentile rank of chance performance in the Dog Owner group?

Answer 15

56

Question 16

7. What is the best available interpretation of just the previous two answers?

Select one:
a. Both groups performed roughly comparably
b. The Non-Dog Owners performed worse than Dog Owners
c. Non-Dog Owners performed about five times better than Dog Owners
d. Non-Dog Owners performed about two times better than Dog Owners
e. Non-Dog Owners performed one question better than Dog Owners

Answer 16

a. Both groups performed roughly comparably

Question 17

7. How many questions higher is the mean of the Non-Dog Owner group than chance?

Answer 17

1.3

Question 18

7. How may questions higher is the mean of the Dog Owner group than chance?

Answer 18

0.24

Question 19

7. What is the best interpretation of just the previous two answers?

Select one:
a. The Non-Dog Owners performed worse than Dog Owners
b. Non-Dog Owners performed about five times better than Dog Owners
c. Non-Dog Owners performed about 0.4 standard units better than Dog Owners
d. Non-Dog Owners performed about two times better than Dog Owners
e. Non-Dog Owners performed about one question better than Dog Owners
f. Both groups performed roughly comparably

Answer 19

e. Non-Dog Owners performed about one question better than Dog Owners

Question 20

7. What is the z-score for the chance number of questions correct in the Non-Dog Owner group?

Answer 20

-0.71

Question 21

7. What is the z-score for the chance number of questions correct in the Dog Owner group?

Answer 21

-0.31

Question 22

7. What is the best interpretation of just the previous two answers?

Select one:
a. The Non-Dog Owners performed worse than Dog Owners
b. Non-Dog Owners performed about five times better than Dog Owners
c. Both groups performed roughly comparably
d. Non-Dog Owners performed about one question better than Dog Owners
e. Non-Dog Owners performed about two times better than Dog Owners
f. Non-Dog Owners performed about 0.4 standard units better than Dog Owners

Answer 22

f. Non-Dog Owners performed about 0.4 standard units better than Dog Owners

Question 23

7. What additional descriptive statistics are relevant for explaining the different interpretations of the three preceding descriptive analyses?

Select one or more:
a. Are the distributions symmetric?
b. Are the sample sizes the same?
c. Are the distributions asymptotic?
d. Are the distributions single-peaked?

Answer 23

a. Are the distributions symmetric?
c. Are the distributions asymptotic?
d. Are the distributions single-peaked?