Use a ?S1U1P12S1S1P0 test to test the claim that in the given contingency table, the row variable and the column variable are independent -The table below shows the age and favorite type of music of 668 randomly selected people. \[\begin{array} { l | r r r } & \text { Rock } & \text { Pop } & \text { Classical } \\ \hline 15 - 25 & 50 & 85 & 73 \\ 25 - 35 & 68 & 91 & 60 \\ 35 - 45 & 90 & 74 & 77 \end{array}\] Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.

H?: Age and preferred music type are ind

A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the flu was recorded. The results are shown below. \[\begin{array} { r | r r r } & \text { Vaccinated } & \text { Placebo } & \text { Control } \\ \hline \text { Caught the flu } & 8 & 19 & 21 \\ \text { Did not catch the flu } & 142 & 161 & 79 \end{array}\] Use a 0.05 significance level to test the claim that the proportion of people catching the flu is the same in all three groups.

@#LAT-DLM& : The proportion of people catching the

Exam 11: Multinomial Experiments and Contingency Tables

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent. Correct Incorrect Math 27 53 English 43 37

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Question 1

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H₀: Major and response are independent.
H₁: Major and response are dependent. Test statistic: $\chi ^ { 2 } = 6.502$ . Critical value: $\chi ^ { 2 } = 2.706$ .
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that response and 1 are independent.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Use a significance level of 0.01 to test the claim that workplace accidents are distributed on workdays as follows: Monday 25%, Tuesday: 15%, Wednesday: 15%, Thursday: 15%, and Friday: 30%. In a study of 100 workplace accidents, 23 occurred on a Monday, 12 occurred on a Tuesday, 12 occurred on a Wednesday, 18 occurred on a Thursday, and 35 occurred on a Friday.

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Question 2

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$\mathrm { H } _ { 0 }$ : Workplace accidents occur according to the stated percentages.
$\mathrm { H } _ { 1 }$ : Workplace accidents do not occur according to the stated percentages.
Test statistic: $\chi ^ { 2 } = 2.793$ . Critical value: $\chi ^ { 2 } = 13.277$ . Fail to reject the null hypothesis. There is not sufficien evidence to warrant rejection of the claim that workplace accidents occur according to the stated percentages.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Use the sample data below to test whether car color affects the likelihood of being in an accident. Use a significance level of 0.01. Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30

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Question 3

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H₀: Car color and being in an accident are independent.
H₁: Car color and being in an accident are dependent. Test statistic: $\chi ^ { 2 } = 0.4287$ . Critical value: $\chi ^ { 2 } = 9.210$ .
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that car c and being in an accident are independent.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Define categorical data and give an example.

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Question 4

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -An observed frequency distribution of exam scores is as follows: nging exam score under60 60-69 70-79 80-89 90-100 frequncy 30 30 140 60 40 i) Assuming a normal distribution with $\mu = 75$ and $\sigma = 15$ , find the probability of a randomly selected subject bel to each class. (Use boundaries of $59.5,69.5,79.5,89.5$ . ) ii) Using the probabilities found in part (i), find the expected frequency for each category. iii) Use a $0.05$ significance level to test the claim that the exam scores were randomly selected from a normally distributed population with $\mu = 75$ and $\sigma = 15$ .

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Question 5

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -In studying the occurrence of genetic characteristics, the following sample data were obtained. At the 0.05 significance level, test the claim that the characteristics occur with the same frequency. Characteristic A B C D E F Frequency 28 30 45 48 38 39

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Question 6

Use a 0.01 significance level to test the claim that the proportion of men who plan to vote in the next election is the same as the proportion of women who plan to vote. 300 men and 300 women were randomly selected and asked whether they planned to vote in the next election. The results are shown below. Men Women Plan to vote 170 185 Do not plan to vote 130 115

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Question 7

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Explain the computation of expected values for contingency tables in terms of probabilities. Refer to the assumptions of the null hypothesis as part of your explanation. You might give a brief example to illustrate.

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Question 8

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05 significance level, test the claim that the treatment (drug or placebo)is independent of the reaction (whether or not headaches were experienced). Drug Placebo Headaches 11 7 No headaches 73 91

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Question 9

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -An observed frequency distribution is as follows: Number of successes 0 1 2 Frequency 41 93 66 i)Assuming a binomial distribution with n = 2 and p = 1/2, use the binomial formula to find the probability corresponding to each category of the table. ii)Using the probabilities found in part (i), find the expected frequency for each category. iii)Use a 0.05 level of significance to test the claim that the observed frequencies fit a binomial distribution for which n = 2 and p = 1/2.

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Question 10

At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The results are given in the table below. Test the hypothesis at the 0.05 level that the proportion of wins is the same for teams wearing suits as for teams wearing jeans. Win Loss Suit 22 28 T-shirt 28 22

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Question 11

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Draw an example of a representative chi-square distribution and discuss three characteristics of a chi-square distribution. Show an example of the special case of the chi-square distribution for only 1 or 2 degrees of freedom.

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Question 12

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Describe the null hypothesis for the test of independence. List the assumptions for the ?2 test of independence. What is the major difference between the assumptions for this test and the assumptions for the previous tests we have studied?

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Question 13

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Responses to a survey question are broken down according to employment status and the sample results are given below. At the 0.10 significance level, test the claim that response and employment status are independent. Yes No Undecided Employed 30 15 5 Unemployed 20 25 10

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Question 14

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -In studying the responses to a multiple-choice test question, the following sample data were obtained. At the 0.05 significance level, test the claim that the responses occur with the same frequency. Response Frequency 12 15 16 18 19

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Question 15

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -The table below shows the age and favorite type of music of 668 randomly selected people. Rock Pop Classical 15-25 50 85 73 25-35 68 91 60 35-45 90 74 77 Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.

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Question 16

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -An observed frequency distribution of exam scores is as follows: nging exam score under60 60-69 70-79 80-89 90-100 frequncy 36 75 85 70 34 i) Assuming a normal distribution with $\mu = 75$ and $\sigma = 15$ , find the probability of a randomly selected subject bel to each class. (Use boundaries of $59.5,69.5,79.5,89.5$ .) ii) Using the probabilities found in part (i), find the expected frequency for each category. iii) Use a $0.05$ significance level to test the claim that the exam scores were randomly selected from a normally distributed population with $\mu = 75$ and $\sigma = 15$ .

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Question 17

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?

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Question 18

A survey conducted in a small town yielded the results shown in the table. Men Women Plan to vote 105 87 Do not plan to vote 312 246 i) Test the claim that the intention to vote in the next presidential election is independent of the gender of the pel being surveyed. Use a $0.05$ significance level. ii) Using Yates' correction, replace $\sum {\frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }}$ with $\sum{\frac { ( | \mathrm { O } - \mathrm { E } | - 0.5 ) ^ { 2 } } { \mathrm { E } }}$ and repeat the test. What effect does Yates correction have on the value of the test statistic?

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Question 19

A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the flu was recorded. The results are shown below. Vaccinated Placebo Control Caught the flu 8 19 21 Did not catch the flu 142 161 79 Use a 0.05 significance level to test the claim that the proportion of people catching the flu is the same in all three groups.

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Question 20

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Define categorical data and give an example.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 11: Multinomial Experiments and Contingency Tables

Use a ?2 test to test the claim that in the given contingency table, the row variable and the column variable are independent -Define categorical data and give an example.

Use a ?2 test to test the claim that in the given contingency table, the row variable and the column variable are independent -Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Define categorical data and give an example.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?