Deck 11: Chi-Square Tests

Question 1

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the test will involve ________ degree(s)of freedom.

Answer 1

1

Question 2

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2, the p-value of the test is ________.

Answer 2

0.0621

Question 3

TABLE 11-1
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 11-1, what is the critical value when performing a chi-square test on whether the population proportions are different if α = 0.05?

A) ±1.645
B) ±1.96
C) 3.841
D) 2.706

Answer 3

3.841

Question 4

The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.

Question 5

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2, the null hypothesis should be rejected.

Question 6

TABLE 11-1
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 11-1, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct?

A) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years.
B) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years.
C) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.
D) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.

Question 7

In testing the difference between two proportions using the normal distribution, we may use either a one-tail chi-square test or two-tail Z test.

Question 8

A test for the difference between two proportions can be performed using the chi-square distribution.

Question 9

If we use the χ² analysis to test for the differences among 4 proportions, the degrees of freedom are equal to ________.

A) 3
B) 4
C) 5
D) 1

Question 10

TABLE 11-1
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 11-1, what is the critical value when testing whether the population proportions are different if α = 0.10?

A) ±1.645
B) ±1.96
C) 3.842
D) 2.706

Question 11

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

Question 12

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2 , the value of the test statistic is ________.

Question 13

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2 , the hypotheses the dean should use are:

A) H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0.
B) H₀: π₁ - π₂ ≠ 0 versus H₁: π₁ - π₂ = 0.
C) H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0.
D) H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0.

Question 14

In testing a hypothesis using the χ² test, the theoretical frequencies are based on the

A) null hypothesis.
B) alternative hypothesis.
C) normal distribution.
D) none of the above

Question 15

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2 , the null hypothesis will be rejected if the test statistic is ________.

Question 16

TABLE 11-2
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
Referring to Table 11-2, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

Question 17

TABLE 11-1
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 11-1, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

A) H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0
B) H₀: π₁ - π₂ ≠ 0 versus H₁: π₁ - π₂ = 0
C) H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0
D) H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0

Question 18

If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is

A) the Z test.
B) the χ² test.
C) both A and B
D) neither A nor B.

Question 19

TABLE 11-1
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 11-1, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using α = 0.10?

A) 4.335
B) 2.706
C) 1.194
D) 0.274

Question 20

A test for whether one proportion is higher than the other can be performed using the chi-square distribution.

Question 21

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the expected cell frequency in the Female/Non-Local cell is ________.

Question 22

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the value of the test statistic is ________.

Question 23

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the expected cell frequency in the Male/Local cell is ________.

Question 24

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the expected cell frequency for the Procedure A/Clear cell is ________.

Question 25

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the test will involve ________ degrees of freedom.

Question 26

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the null hypothesis will be rejected.

Question 27

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the overall or mean proportion of clear operations is ________.

Question 28

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the value of the test statistic is ________.

Question 29

TABLE 11-4
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
Referring to Table 11-4, the calculated value of the test statistic is ________.

A) -0.1777
B) -0.0185
C) 1.4999
D) 1.5190

Question 30

TABLE 11-4
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
Referring to Table 11-4, at 1% level of significance,

A) there is sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
B) there is insufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
C) there is sufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.
D) there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.

Question 31

TABLE 11-4
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
Referring to Table 11-4, which test would be used to properly analyze the data in this experiment?

A) χ² test of independence
B) χ² test for difference among more than two proportions
C) χ² test for difference between two proportions
D) none of the above

Question 32

TABLE 11-4
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
Referring to Table 11-4, the critical value of the test statistic at 1% level of significance is ________.

A) 7.7794
B) 13.2767
C) 20.0902
D) 23.2093

Question 33

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the critical value of the test is ________.

Question 34

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the decision made suggests that the four procedures all have different proportions of clear operations.

Question 35

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the critical value of the test is ________.

Question 36

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes.

Question 37

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the expected cell frequency for the Procedure D/Return cell is ________.

Question 38

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the overall or mean proportion of local riders is ________.

Question 39

TABLE 11-3
The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Table 11-3, the null hypothesis will be rejected.

Question 40

TABLE 11-4
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.
Referring to Table 11-4, the degrees of freedom of the test statistic is ________.

A) 4
B) 8
C) 10
D) 448

Question 41

TABLE 11-5
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 11-5, the decision made suggests that the four procedures do not all have the same proportion of clear operations.

Question 42

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the critical value of the test is ________.

Question 43

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the critical value?

Question 44

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the p-value of the test statistic?

Question 45

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the null hypothesis will be rejected.

Question 46

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the form of the alternative hypothesis?

A) H₀: π₁ ≠ π₂ ≠ π₃
B) H₀: π₁ ≠ π₂ = π₃
C) H₀: π₁ = π₂ ≠ π₃
D) H₁: not all πⱼ are the same

Question 47

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the correct conclusion?

A) There is enough evidence that the proportions are all different in the three years.
B) There is not enough evidence that the proportions are all different in the three years.
C) There is enough evidence that at least two of the proportions are not equal.
D) There is not enough evidence that at least two of the proportions are not equal.

Question 48

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the decision made suggests that the three cities all have different proportions of hotels that correctly post minibar charges.

Question 49

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what are the degrees of freedom of the test statistic?

Question 50

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the value of the test statistic?

Question 51

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, the null hypothesis cannot be rejected.

Question 52

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years?

Question 53

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the expected number of shoppers who do not pay by check in year 3 if there is no difference in the proportion of shoppers who pay by check among the three years?

Question 54

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, what is the form of the null hypothesis?

A) H₀: π₁ = π₂ = π₃
B) H₀: π₁ = π₂ ≠ π₃
C) H₀: π₁ ≠ π₂ = π₃
D) H₀: π₁ ≠ π₂ ≠ π₃

Question 55

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the expected cell frequency for the Hong Kong/Yes cell is ________.

Question 56

TABLE 11-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 11-6, the assumptions needed to perform the test are satisfied.

Question 57

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the test will involve ________ degrees of freedom.

Question 58

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the expected cell frequency for the Paris/No cell is ________.

Question 59

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the decision made suggests that the three cities do not all have the same proportion of hotels that correctly post minibar charges.

Question 60

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Table 11-7, the value of the test statistic is ________.

Question 61

TABLE 11-11
The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table:

He will use this table to do a chi-square test of independence with a level of significance of 0.01.
Referring to Table 11-11, the test will involve ________ degrees of freedom.

Question 62

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
If we use the chi-square method of analysis to test for the difference between proportions, we must assume that there are at least 5 observed frequencies in each cell of the contingency table.

Question 63

TABLE 11-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Referring to Table 11-10, find the rejection region necessary for testing at the 0.05 level of significance whether there is a relationship between defect rate and years of experience.

A) Reject H₀ if χ² > 16.919.
B) Reject H₀ if χ² > 15.507.
C) Reject H₀ if χ² > 11.143.
D) Reject H₀ if χ² > 9.488.

Question 64

TABLE 11-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Referring to Table 11-10, for the cell with 1 to 4 years of training time and a high defect rate, what is the contribution to the overall χ² statistic for the independence test?

A) 0.36
B) 0.1296
C) 0.015
D) 0.0144

Question 65

TABLE 11-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Referring to Table 11-10, a test was conducted to determine if a relationship exists between defect rate and years of experience. Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at α = 0.05.

A) 0.045
B) 0.055
C) 0.074
D) 0.080

Question 66

TABLE 11-11
The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table:

He will use this table to do a chi-square test of independence with a level of significance of 0.01.
Referring to Table 11-11, the critical value of the test is ________.

Question 67

TABLE 11-9
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 11-9, the degrees of freedom of the test statistic are ________.

A) 1
B) 2
C) 4
D) 299

Question 68

TABLE 11-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Referring to Table 11-10, which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience?

A) χ² test for independence
B) χ² test for differences among more than two proportions
C) χ² test for variance
D) none of the above

Question 69

TABLE 11-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Referring to Table 11-10, what is the expected number of employees with 1 to 4 years of training time and a high defect rate?

A) 12.00
B) 8.64
C) 6.67
D) 6.00

Question 70

TABLE 11-9
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 11-9, at 5% level of significance, the conclusion is that

A) brand awareness of female TV viewers and the gender of the spokesperson are independent.
B) brand awareness of female TV viewers and the gender of the spokesperson are not independent.
C) brand awareness of female TV viewers and the gender of the spokesperson are related.
D) both B and C

Question 71

TABLE 11-9
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 11-9, at 5% level of significance, the critical value of the test statistic is ________.

A) 3.8415
B) 5.9914
C) 9.4877
D) 13.2767

Question 72

TABLE 11-8
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles in San Diego County depends on ethnic status. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Referring to Table 11-8, which test would be used to properly analyze the data in this experiment?

A) χ² test for independence
B) χ² test for differences among more than two proportions
C) χ² test for variance
D) none of the above

Question 73

TABLE 11-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period, any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Referring to Table 11-10, what is the expected number of employees with less than 1 year of training time and a high defect rate?

A) 4.17
B) 4.60
C) 5.28
D) 9.17

Question 74

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
When using the χ² test for independence, you should be aware that expected frequencies that are too small will lead to a large Type I error.

Question 75

TABLE 11-9
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 11-9, which test would be used to properly analyze the data in this experiment?

A) χ² test for independence
B) χ² test for differences among more than two proportions
C) χ² test for variance
D) none of the above

Question 76

TABLE 11-8
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles in San Diego County depends on ethnic status. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Referring to Table 11-8, at 5% level of significance, there is sufficient evidence to conclude that

A) use of seat belts in motor vehicles is related to ethnic status in San Diego County.
B) use of seat belts in motor vehicles depends on ethnic status in San Diego County.
C) use of seat belts in motor vehicles is associated with ethnic status in San Diego County.
D) all of the above

Question 77

TABLE 11-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom.

A) 5
B) 6
C) 7
D) 12

Question 78

TABLE 11-8
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles in San Diego County depends on ethnic status. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Referring to Table 11-8, the calculated test statistic is ________.

A) -0.9991
B) -0.1368
C) 48.1849
D) 72.8063

Question 79

TABLE 11-8
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles in San Diego County depends on ethnic status. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Referring to Table 11-8, at 5% level of significance, the critical value of the test statistic is ________.

A) 3.8415
B) 5.9914
C) 9.4877
D) 13.2767

Question 80

TABLE 11-9
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 11-9, the calculated test statistic is ________.

A) -0.1006
B) 0.00
C) 5.9418
D) 6.1194