Exam 11: Chi-Square and Analysis of Variance

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

A survey conducted in a small business yielded the results shown in the table. Men Women Health insurance 50 20 No health insurance 30 10 Test the claim that health care coverage is independent of gender. Use a $0.05$ significance level. What is the value of the test statistic?

Goodness-of-fit hypothesis tests are always___________________.

Perform the indicated goodness-of-fit test. You roll a die 48 times with the following results. Number 1 2 3 4 5 6 Frequency 4 13 2 14 13 2 Use a significance level of 0.05 to test the claim that the die is fair.

Define categorical data and give an example.

While conducting a goodness-of-fit test if the observed and expected values are close, you would expect which of the following:

Describe the null hypothesis for the test of independence. List the assumptions for the $\chi ^ { 2 }$ test of independence.

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.

Describe a goodness-of-fit test. What assumptions are made when using a goodness-of-fit test?

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

Perform the indicated goodness-of-fit test. 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 Thurs Fri Absences 37 15 12 23 43

Use a $\chi ^ { 2 }$ 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 50 85 73 68 91 60 90 74 77 Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.

In studying the occurrence of genetic characteristics, the following sample data were obtained. You would like to test the claim that the characteristics occur with the same Frequency at the 0.05 significance level. What is value of the test statistic? Characteristic A B C D E F Frequency 28 30 45 48 39 39

Perform the indicated goodness-of-fit test. 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 $\chi ^ { 2 }$ 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

A survey of students at a college was asked if they lived at home with their parents, rented an apartment, or owned their own home. The results are shown in the table below sorted by gender. At $\alpha = 0.10$ , test the claim that living accommodations are independent of the gender of the student. Live with Parent Rent Apartment Own Home Male 20 26 19 Female 22 28 26

The following table represents the number of absences on various days of the week at an elementary school. Monday Tuesday Wednesday Thursday Friday 45 32 17 25 38 Identify the number of degrees of freedom for a goodness-of-fit test (for a uniform Distribution), assuming a 0.05 significance level.

The following table represents the number of absences on various days of the week at an elementary school. Monday Tuesday Wednesday Thursday Friday 45 32 17 25 38 Identify the critical value for a goodness-of-fit test, assuming a $0.05$ significance level.

Which of the following is not a characteristic of a chi-square distribution?

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