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 -A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled. Day Mon Tue Wed Thur Fri Absences 37 15 12 23 43

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 1000 subjects has a distribution that agrees with the distribution of state populations.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -The following table shows the number of employees who called in sick at a business for different days of a particular week. Day Sun Mon tues Wed Thurs Fri Sat Number sick 8 12 7 11 9 11 12 i)At the 0.05 level of significance, test the claim that sick days occur with equal frequency on the different days of the week. ii)Test the claim after changing the frequency for Saturday to 152. Describe the effect of this outlier on the test.

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -You roll a die 48 times with the following results. Number 1 2 3 4 5 6 Frequency 14 4 2 1 12 15 Use a significance level of 0.05 to test the claim that the die is fair.

A survey conducted in a small business yielded the results shown in the table. Men Women Health insurance 41 22 No health insurance 34 24 i) Test the claim that health care coverage is independent of gender. 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?

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -In the chi-square test of independence, the formula used is $\chi ^ { 2 } = \frac { \Sigma ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ . Discuss the meaning of $\mathrm { O }$ and $\mathrm { E }$ and explain the circumstances under which the $\chi ^ { 2 }$ values will be smaller or larger. What is the relationship between a significant $\chi ^ { 2 }$ value and the values of $\mathrm { O }$ and $\mathrm { E }$ ?

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 test of homogeneity. What characteristic distinguishes a test of homogeneity from a test of independence?

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent -Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. Response A B C D E Frequency 12 15 16 18 19

A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below. College A College B College C College D Smoke 17 26 11 34 Don't smoke 83 74 89 66 Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges.

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 47 98 55 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 w 2 and $p = 1 / 2$ =

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 gender and the sample results are given below. At the 0.05 significance level, test the claim that response and gender are independent. Yes No Undecided Male 25 50 15 Female 20 30 10