Exam 11: Goodness-Of-Fit and Contingency Tables

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

A researcher wishes to test whether the proportion of college students who smoke is the same at 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.

The table in number 18 is called a two-way table. Why is the terminology of two-way table used?

Responses to a survey question about color preference for a candy are broken down according to gender in the table given below. At the 0.05 significance level, test the claim that candy color preference and gender are independent. Red Blue Yellow Male 25 50 15 Female 20 30 10 What is your conclusion about the null hypothesis and about the claim?

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

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 Frequency 12 15 16 18 19

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

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

A table summarizes the success and failures when subjects used different methods (yoga, acupuncture, and chiropractor) to relieve back pain. If we test the claim at a 5% level of significance that success is independent of the method used, technology provides a P-value of 0.0655 . What does the P-value tell us about the claim?

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 claim 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 What is your conclusion about the null hypothesis?

A table summarizes the success and failures when subjects used different methods (yoga, acupuncture, and chiropractor)to relieve back pain. If we test the claim at a 5% level of significance that success is independent of the method used, technology provides a P-value Of 0.0355. What does the P-value tell us about the claim?

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

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.

Discuss the three characteristics of a chi-square distribution.

The table in number 18 is called a two-way table. Why is the terminology of two-way table used?

Discuss the three characteristics of a chi-square distribution

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 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?

Use a $x ^ { 2 }$ 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. Men Women Plan to vote 170 185 Do not plan to vote 130 115 Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.