The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. \[\begin{array}{l} \begin{array} { l | c c c } & { \text { Opinion } } \\ \hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \\ \text { Republican } & 42 & 20 & 14 \\ \text { Democrat } & 50 & 24 & 18 \\ \text { Independent } & 10 & 16 & 6 \end{array}\\ \text { Find the chi-square test statistic } x ^ { 2 } \text { used to test the claim of independence. } \end{array}\]

A) 7.662 B) 11.765 C) 9.483 D) 8.030 A) 7.662 B) 11.765 C) 9.483 D) 8.030

A multinomial experiment with $k = 3$ cells and $n = 100$ has been conducted and the results are shown in the table. $\begin{array}{l} \quad\quad\text { Cell }\\ \begin{array} { c | c c c } & 1 & 2 & 3 \\ \hline n _ { i } & 46 & 32 & 22 \end{array} \end{array}$ Construct a 99% confidence interval for the multinomial probability associated with cell 2.

The answer of A multinomial experiment with $k = 3$...

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. $\begin{array}{l|l} \text { RESPONSE } & \text { NUMBER } \\ \hline \text { Agree Strongly } & 60 \\ \text { Agree Somewhat } & 110 \\ \text { Disagree Somewhat } & 80 \\ \text { Disagree Strongly } & 50 \end{array}$ In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation?

A) $\mathrm { E } _ { 1 } = 75 , \mathrm { E } _ { 2 } = 75 , \mathrm { E } _ { 3 } = 75 , \mathrm { E } _ { 4 } = 75$ B) $\mathrm { E } _ { 1 } = 300 , \mathrm { E } _ { 2 } = 300 , \mathrm { E } _ { 3 } = 300 , \mathrm { E } _ { 4 } = 300$ C) $\mathrm { E } _ { 1 } = 0.25 , \mathrm { E } _ { 2 } = 0.25 , \mathrm { E } _ { 3 } = 0.25 , \mathrm { E } _ { 4 } = 0.25$ D) $\mathrm { E } _ { 1 } = 60 , \mathrm { E } _ { 2 } = 110 , \mathrm { E } _ { 3 } = 80 , \mathrm { E } _ { 4 } = 50$ A) $\mathrm { E } _ { 1 } = 75 , \mathrm { E } _ { 2 } = 75 , \mathrm { E } _ { 3 } = 75 , \mathrm { E } _ { 4 } = 75$ B) $\mathrm { E } _ { 1 } = 300 , \mathrm { E } _ { 2 } = 300 , \mathrm { E } _ { 3 } = 300 , \mathrm { E } _ { 4 } = 300$ C) $\mathrm { E } _ { 1 } = 0.25 , \mathrm { E } _ { 2 } = 0.25 , \mathrm { E } _ { 3 } = 0.25 , \mathrm { E } _ { 4 } = 0.25$ D) $\mathrm { E } _ { 1 } = 60 , \mathrm { E } _ { 2 } = 110 , \mathrm { E } _ { 3 } = 80 , \mathrm { E } _ { 4 } = 50$

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. \[\begin{array} { l | l } \text { RESPONSE } & \text { NUMBER } \\ \hline \text { Agree Strongly } & 60 \\ \text { Agree Somewhat } & 110 \\ \text { Disagree Somewhat } & 80 \\ \text { Disagree Strongly } & 50 \end{array}\] In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a 95% confidence interval for the multinomial probability associated with the "Agree Strongly" response was desired. Which of the following confidence intervals should be used?

A) (0.141, 0.259) B) (0.162, 0.238) C) (0.145, 0.255) D) (0.155, 0.245) A) (0.141, 0.259) B) (0.162, 0.238) C) (0.145, 0.255) D) (0.155, 0.245)

Test the null hypothesis of independence of the two classifications, $A$ and $B$, of the $3 \times 3$ contingency table shown below. Test using $\alpha = .025$. $\begin{array} { l l | l l l } & &{ \quad\mathrm { B } } \\ & & \mathrm { B } _ { 1 } & \mathrm {~B} _ { 2 } & \mathrm {~B} _ { 3 } \\ \hline & \mathrm { A } _ { 1 } & 19 & 40 & 60 \\ \mathrm {~A} & \mathrm {~A} _ { 2 } & 55 & 23 & 22 \\ & \mathrm {~A} _ { 3 } & 31 & 42 & 47 \end{array}$

The answer of Test the null hypothesis of independence of...

Exam 10: Categorical Data Analysis

A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan)do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are summarized below. The goal of the analysis is to determine if the proportions of entrepreneurs Who drive American, European, and Japanese cars differ. U.S. Europe Japan 40 35 25 In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. Suppose the p-value for the test was calculated to be $\mathrm { p } = 0.1738$ . What is the appropriate conclusion to make when testing at $\alpha = 0.10$ ?

(Multiple Choice)

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Question 21

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 Find the chi-square test statistic used to test the claim of independence.

(Multiple Choice)

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Question 22

A multinomial experiment with $k = 3$ cells and $n = 100$ has been conducted and the results are shown in the table. Cell 1 2 3 46 32 22 Construct a 99% confidence interval for the multinomial probability associated with cell 2.

(Essay)

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Question 23

When using any procedure to perform a hypothesis test, the user should always be certain that the experiment satisfies the assumptions given with the procedure.

(True/False)

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Question 24

A teacher finds that final grades in the statistics department are distributed as: A, 25\%; B, 25\%; C, $40 \%$ ; D, 5\%; F, 5\%. At the end of a randomly selected semester, the following grades were recordec Find the rejection region used to determine if the grade distribution for the department is different than expected. Use $\alpha = 0.01$ . Grade A B C D F Number 42 36 60 14 8

(Multiple Choice)

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Question 25

A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the probabilities show no preference. Us $\alpha = 0.01$ Brand 1 2 3 4 5 Customers 18 32 55 65 30

(Essay)

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Question 26

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE NUMBER Agree Strongly 60 Agree Somewhat 110 Disagree Somewhat 80 Disagree Strongly 50 In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation?

(Multiple Choice)

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Question 27

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliations. Assuming the row and column classifications are independent, find an estimate for the expected Cell count $E _ { 22 }$ Opinion Party Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6

(Multiple Choice)

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Question 28

A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the giver categories is $18 \%$ for the under 26 group, $39 \%$ for the $26 - 45$ group, $31 \%$ for the 45 - 65 group, and $12 \%$ for the group over 65 . Find the rejection region used to test the claim that all ages have crash rates proportional to their number of drivers. Use $\alpha = 0.05$ . Age Under 26 26-45 46-65 Over 65 Drivers 66 39 25 30

(Multiple Choice)

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Question 29

A random sample of 160 car accidents are selected and categorized by the age of the driver determined to be at fault. The results are listed below. The age distribution of drivers for the given categories is $18 \%$ for the under 26 group, $39 \%$ for the 26-45 group, $31 \%$ for the $45 - 65$ group, and $12 \%$ for the group over 65 . Calculate the chi-square test statistic $\chi ^ { 2 }$ used to test the claim that all ages have crash rates proportional to their driving rates. Age Under 26 26-45 46-65 Over 65 Drivers 66 39 25 30

(Multiple Choice)

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Question 30

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE NUMBER Agree Strongly 60 Agree Somewhat 110 Disagree Somewhat 80 Disagree Strongly 50 In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. Which of the following statements is not necessary for the analysis to be valid?

(Multiple Choice)

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Question 31

A survey of entrepreneurs focused on their job characteristics, work habits, social activities, leisure time, etc. One question put to each entrepreneur was, "What make of car (U.S., Europe, or Japan) do you drive?" The responses (number in each category) for a sample of 100 entrepreneurs are Summarized below. The goal of the analysis is to determine if the proportions of entrepreneur who drive American, European, and Japanese cars differ. U.S. Europe Japan 40 35 25 In order to determine whether the true proportions in each response category differ, a one-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation?

(Multiple Choice)

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Question 32

Economists at USF are researching the problem of absenteeism at U.S. firms. A random sample of 100 U.S. organizations was selected to participate in a 1-year study. As part of the study, the economists had collected data on the following two variables for each company: shiftwork available (Yes or No), and union-management relationship (Good or Poor). As part of their analyses, the economists wanted to determine whether or not a company makes shiftwork available depends on the relationship between union and management. The collected data are Shown below: Relation Shiftwork Good Bad Total No 11 22 33 Yes 25 42 67 Total 36 64 100 In order to determine whether the shiftwork responses depend on the relationship responses, a two-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation?

(Multiple Choice)

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Question 33

Describe probabilities of the k outcomes of the multinomial experiment trials.

(Essay)

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Question 34

Inc. Technology reported the results of consumer survey in which 300 Internet users indicated their level of agreement with the following statement: "The government needs to be able to scan Internet messages and user communications to prevent fraud and other crimes." The possible responses were "agree strongly", "agree somewhat", "disagree somewhat", and "disagree strongly". The number of Internet users in each category is summarized in the table. RESPONSE NUMBER Agree Strongly 60 Agree Somewhat 110 Disagree Somewhat 80 Disagree Strongly 50 In order to determine whether the true proportions of Internet users in each response category differ, a one-way chi-square analysis should be conducted. As part of that analysis, a 95% confidence interval for the multinomial probability associated with the "Agree Strongly" response was desired. Which of the following confidence intervals should be used?

(Multiple Choice)

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Question 35

Use the appropriate table to find the following probabili $: P \left( \chi ^ { 2 } \leq 13.277 \right) \text { for } d f = 4$

(Multiple Choice)

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Question 36

A business professor conducted a campus survey to estimate demand among all students for a protein supplement for smoothies and other nutritional drinks. Each of 113 students, randomly selected from all students on campus, provided the following information: (1) How health conscious are you? (Very, Moderately, Slightly, Not very) (2) Do you prefer protein supplements in your smoothies? (Yes, No) As part of his analysis, the professor claims that whether or not the student prefers a protein supplement in smoothies is independent of health consciousness level (Very, Moderate, Slightly, or not very). Use the chi-square distribution to determine the rejection region for this test when Testing at $\alpha = 0.05$

(Multiple Choice)

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Question 37

In a test of independence, it is safe to conclude that the events are independent when the value of $? ^ { 2 }$ is very small.

(True/False)

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Question 38

A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Test the claim that the number of home team and visiting team wins is independent of the sport. Use $\alpha = 0.01$ Football Basketball Soccer Baseball Home team wins 39 156 25 83 Visiting team wins 31 98 19 75

(Essay)

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Question 39

Test the null hypothesis of independence of the two classifications, $A$ and $B$ , of the $3 \times 3$ contingency table shown below. Test using $\alpha = .025$ . 19 40 60 55 23 22 31 42 47

(Essay)

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Question 40

A multinomial experiment with $k = 3$ cells and $n = 100$ has been conducted and the results are shown in the table. Cell 1 2 3 46 32 22 Construct a 99% confidence interval for the multinomial probability associated with cell 2.

When using any procedure to perform a hypothesis test, the user should always be certain that the experiment satisfies the assumptions given with the procedure.

A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the probabilities show no preference. Us $\alpha = 0.01$ Brand 1 2 3 4 5 Customers 18 32 55 65 30

Describe probabilities of the k outcomes of the multinomial experiment trials.

Use the appropriate table to find the following probabili $: P \left( \chi ^ { 2 } \leq 13.277 \right) \text { for } d f = 4$

In a test of independence, it is safe to conclude that the events are independent when the value of $? ^ { 2 }$ is very small.

Test the null hypothesis of independence of the two classifications, $A$ and $B$ , of the $3 \times 3$ contingency table shown below. Test using $\alpha = .025$ . 19 40 60 55 23 22 31 42 47

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Exam 10: Categorical Data Analysis

A multinomial experiment with k=3k = 3k=3 cells and n=100n = 100n=100 has been conducted and the results are shown in the table. Cell 1 2 3 46 32 22 Construct a 99% confidence interval for the multinomial probability associated with cell 2.

When using any procedure to perform a hypothesis test, the user should always be certain that the experiment satisfies the assumptions given with the procedure.

A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the probabilities show no preference. Us α=0.01\alpha = 0.01α=0.01 Brand 1 2 3 4 5 Customers 18 32 55 65 30

Describe probabilities of the k outcomes of the multinomial experiment trials.

Use the appropriate table to find the following probabili :P(χ2≤13.277) for df=4: P \left( \chi ^ { 2 } \leq 13.277 \right) \text { for } d f = 4:P(χ2≤13.277) for df=4

In a test of independence, it is safe to conclude that the events are independent when the value of ?2? ^ { 2 }?2 is very small.

Test the null hypothesis of independence of the two classifications, AAA and BBB , of the 3×33 \times 33×3 contingency table shown below. Test using α=.025\alpha = .025α=.025 . 19 40 60 55 23 22 31 42 47

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

A multinomial experiment with $k = 3$ cells and $n = 100$ has been conducted and the results are shown in the table. Cell 1 2 3 46 32 22 Construct a 99% confidence interval for the multinomial probability associated with cell 2.

A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Test the claim that the probabilities show no preference. Us $\alpha = 0.01$ Brand 1 2 3 4 5 Customers 18 32 55 65 30

Use the appropriate table to find the following probabili $: P \left( \chi ^ { 2 } \leq 13.277 \right) \text { for } d f = 4$

In a test of independence, it is safe to conclude that the events are independent when the value of $? ^ { 2 }$ is very small.

Test the null hypothesis of independence of the two classifications, $A$ and $B$ , of the $3 \times 3$ contingency table shown below. Test using $\alpha = .025$ . 19 40 60 55 23 22 31 42 47