Deck 15: Chi-Square Tests

Question 1

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the expected cell frequency in the Female/Non-Local cell is _______.

Answer 1

31.02

Question 2

Instruction 15-2
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 Instruction 15-2,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.

Answer 2

A

Question 3

Instruction 15-2
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 Instruction 15-2,the p-value of the test is _______.

Answer 3

0.0621

Question 4

Instruction 15-2
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 Instruction 15-2,the null hypothesis will be rejected if the test statistic is_______.

Question 5

Instruction 15-2
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 Instruction 15-2,the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

Question 6

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the overall or mean proportion of local riders is _______.

Question 7

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the critical value of the test is _______.

Question 8

Instruction 15-2
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 Instruction 15-2,the value of the test statistic is _______.

Question 9

Instruction 15-1
A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively.
Referring to Instruction 15-1,what is the critical value when performing a chi-square test on whether population proportions are different if α = 0.05?

A) ± 1.645
B) ± 1.96
C) 2.706
D) 3.842

Question 10

Instruction 15-2
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 Instruction 15-2,the null hypothesis should be rejected.

Question 11

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the null hypothesis will be rejected.

Question 12

Instruction 15-2
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 Instruction 15-2,the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

Question 13

Instruction 15-1
A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively.
Referring to Instruction 15-1,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 14

Instruction 15-1
A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively.
Referring to Instruction 15-1,the organization 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) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a professional-development course has increased over the intervening 10 years.
B) Reject the null hypothesis and conclude that the proportion of employees who are interested in a professional-development course has changed over the intervening 10 years.
C) Reject the null hypothesis and conclude that the proportion of employees who are interested in a professional-development 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 professional-development course has not changed over the intervening 10 years.

Question 15

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the expected cell frequency in the Male/Local cell is _______.

Question 16

Instruction 15-1
A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively.
Referring to Instruction 15-1,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) 1.194
B) 0.274
C) 4.335
D) 2.706

Question 17

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the test will involve _______degree(s)of freedom.

Question 18

Instruction 15-1
A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively.
Referring to Instruction 15-1,what is the critical value when testing whether population proportions are different if α = 0.10?

A) 2.706
B) ± 1.645
C) 3.842
D) ± 1.96

Question 19

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

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

Question 20

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes.

Question 21

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

Question 22

When using the χ² tests for independence,you should be aware that expected frequencies that are too small will lead to a large Type I error.

Question 23

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the critical value of the test is _______.

Question 24

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

Question 25

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the expected cell frequency for the Procedure D/Return cell is _______.

Question 26

If you use the χ² method of analysis to test for the differences among four proportions,the degrees of freedom are equal to

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

Question 27

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the overall or mean proportion of clear operations is _______.

Question 28

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the test will involve _______ degree(s)of freedom.

Question 29

Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.

-Referring to Instruction 15-5,the calculated value of the test statistic is

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

Question 30

Instruction 15-4
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
| Average time spent reading story books |
$$\begin{array} { | l | c | c | c | } \hline \begin{array} { l } \text { average time spent } \\\text { watching TV }\end{array} & \begin{array} { c } \text { Less than } \\1 \text { hour }\end{array} & \begin{array} { c } \text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array} { c } \text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than } 2 \text { hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}$$

-Referring to Instruction 15-4,how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average?

A) 687
B) 8
C) 175
D) 130

Question 31

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,which of the following tests will be the most appropriate to find out which of the four procedures is the most effective?

A) The Marascuilo procedure
B) X² test for difference in proportions
C) Z for difference in proportions
D) None of the above

Question 32

Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.

-Referring to Instruction 15-5,the degrees of freedom of the test statistic is

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

Question 33

Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.

-Referring to Instruction 15-5,which test would you use to properly analyse the data in this experiment?

A) (?)² test for difference between two proportions
B) ( ?)² test for difference among more than two proportions
C) (?)² test of independence
D) None of the above

Question 34

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

Question 35

Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.

-Referring to Instruction 15-5,the critical value of the test statistic at 1% level of significance is

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

Question 36

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the expected cell frequency for the Procedure A/Clear cell is_______.

Question 37

Instruction 15-5
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Memory Location } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the five memory locations differ.

-Referring to Instruction 15-5,at 1% level of significance

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

Question 38

Instruction 15-3
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:
$$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Female } & \text { Total } \\\hline \text { Local } & 27 & 44 & 71 \\\hline \text { Non-Local } & 33 & 25 & 58 \\\hline \text { Total } & 60 & 69 & 129 \\\hline\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Instruction 15-3,the value of the test statistic is _______.

Question 39

Instruction 15-4
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
| Average time spent reading story books |
$$\begin{array} { | l | c | c | c | } \hline \begin{array} { l } \text { average time spent } \\\text { watching TV }\end{array} & \begin{array} { c } \text { Less than } \\1 \text { hour }\end{array} & \begin{array} { c } \text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array} { c } \text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than } 2 \text { hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}$$

-Referring to Instruction 15-4,how many children in the survey spent less than 2 hours watching TV and no more than 2 hours reading storybooks on average?

A) 687
B) 175
C) 8
D) 130

Question 40

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

Question 41

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the form of the null hypothesis?

A)H₀: $\pi$ ₁ $\pi$ $\neq$ ₂ = $\pi$ ₃
B)H₀: $\pi$ ₁ = $\pi$ ₂ $\neq$ $\pi$ ₃
C)H₀: $\pi$ ₁ = $\pi$ ₂ $\neq$ $\pi$ ₃
D)H₀: $\pi$ ₁ = $\pi$ ₂ = $\pi$ ₃

Question 42

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure C using a 0.05 level of significance?

Question 43

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure B and procedure D are different at a 0.05 level of significance.

Question 44

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,the assumptions needed to perform the tests are satisfied.

Question 45

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure A and procedure B are different at a 0.05 level of significance.

Question 46

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the correct conclusion?

A) There is enough evidence that at least two of the proportions are not equal.
B) There is not enough evidence that at least two of the proportions are not equal.
C) There is not enough evidence that the proportions are all different in the 3 years.
D) There is enough evidence that the proportions are all different in the 3 years.

Question 47

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure B and procedure D using a 0.05 level of significance?

Question 48

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the decision made suggests that the four procedures do not all have the same proportion of clear operations.

Question 49

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure C and procedure D using a 0.05 level of significance?

Question 50

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure C and procedure D are different at a 0.05 level of significance.

Question 51

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure A and procedure D are different at a 0.05 level of significance.

Question 52

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure A and procedure C are different at a 0.05 level of significance.

Question 53

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the value of the test statistic is _______.

Question 54

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure B and procedure C using a 0.05 level of significance?

Question 55

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure B using a 0.05 level of significance?

Question 56

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the null hypothesis will be rejected.

Question 57

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure D using a 0.05 level of significance?

Question 58

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the form of the alternative hypothesis?

A)H₁: $\pi$ ₁ $\neq$ $\pi$ ₂ = $\pi$ ₃
B)H₁: $\pi$ ₁ = $\pi$ ₂ $\neq$$\pi$ ₃
C)H₁: $\pi$ ₁ $\neq$ $\pi$ ₂ $\neq$$\pi$ ₃
D)H₁: not all $\pi$ _j are the same

Question 59

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,the decision made suggests that the four procedures all have different proportions of clear operations.

Question 60

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.

-Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure B and procedure C are different at a 0.05 level of significance.

Question 61

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 2 and year 3 using a 0.05 level of significance?

Question 62

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,there is not sufficient evidence to conclude that the proportions between year 1 and year 3 are different at a 0.05 level of significance.

Question 63

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the null hypothesis will be rejected.

Question 64

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,the null hypothesis cannot be rejected.

Question 65

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the expected number of shoppers who pay by cheque in year 1 if there is no difference in the proportion of shoppers who pay by cheque among the three years?

Question 66

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the expected cell frequency for the Hong Kong/Yes cell is _______.

Question 67

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,there is sufficient evidence to conclude that the proportions between year 2 and year 3 are different at a 0.05 level of significance.

Question 68

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,there is sufficient evidence to conclude that the proportions between year 1 and year 2 are different at a 0.05 level of significance.

Question 69

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the critical value?

Question 70

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the test will involve _______ degree(s)of freedom.

Question 71

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the decision made suggests that the three cities all have different proportions of hotels that correctly post minibar charges.

Question 72

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the value of the test statistic?

Question 73

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what are the degrees of freedom of the test statistic?

Question 74

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the expected number of shoppers who do not pay by cheque in year 3 if there is no difference in the proportion of shoppers who pay by cheque among the three years?

Question 75

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 2 using a 0.05 level of significance?

Question 76

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the critical value of the test is _______.

Question 77

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the expected cell frequency for the Paris/No cell is_______

Question 78

Instruction 15-8
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.
$$\begin{array} { | c | c | c | c | } \hline & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \text { Yes } & 86 \% & 65 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \% \\\hline\end{array}$$ 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 Instruction 15-8,the value of the test statistic is _______

Question 79

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 3 using a 0.05 level of significance?

Question 80

Instruction 15-7
According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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.
$$\begin{array} { | l | c | c | c | } \hline \text { Cheque Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 175 & 125 \\\hline\end{array}$$

-Referring to Instruction 15-7,what is the p-value of the test statistic?