Exam 11: Chi-Square and Analysis of Variance

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.

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 $\alpha$ = 0.05, 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 18 28 26

Select the null hypothesis for a test of independence.

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. 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.

Discuss the three characteristics of a chi-square distribution.

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

Use a $X^2$ 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

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.

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

Which statement is not true for goodness-of -fit tests?

Define categorical data and give an example.

Discuss the three characteristics of a chi-square distribution._

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

True or False: For a test of independence, the population that the data has come from must be normally distributed.

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.

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 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?

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

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

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