Inference: Chi-Square: 1-7

The attached table shows the number of students referred for disciplinary reasons to the principal's office, broken down by the day of the week. A counselor would like to know if such referrals are related to the day for the week. What is the value of the chi-square statistic for the appropriate test?

• The test proves the geneticist's claim.

• The test proves the geneticist's claim is false.

• The test does not give sufficient evidence to reject the geneticist's claim.

• The test gives sufficient evidence to reject the geneticist's claim.

• The test is inconclusive.

Last year, the audience percentages captured by major news programs were as follows: (ABC, NBC, CBS): 36%, CNN: 42%, FOX:22%. In a random sample of 50 viewers this year, 23 watched (ABC, NBC, CBS), 17 watched CNN, and 10 watched FOX. If a goodness-of-fit test were performed, what would be the p-value?

In the attached table, what value of n results in a table showing perfect independence?

• 30

• 50

• 70

• 75

• 100

A small appliance manufacturer sets up three locations to provide service for its customers. Logs are kept noting whether or not calls about problems are solved successfully. Data from a sample of 500 calls are summarized in the attached table.

Assuming there is no association between location and whether or not a problem is resolved successfully, that is, H₀: independence, what is the expected number of successful calls (problem solved) from Location 2?

Which of the following is the proper use of a chi-square test of independence?

• To test whether the distribution of counts on a categorical variable matches a claimed distribution

• To test whether the distribution of counts on a numerical variable matches a claimed distribution

• To test whether the distribution of two different groups on the same categorical variable matches

• To test whether two categorical variables on the same subjects are related

• To test whether two numerical variables on the same subject are related

Answer explanation

Chi-square tests are for categorical data; in particular, the chi-square test for independence looks at one group of subject cross-classified by two categorical variables.

Which of the following is not true with regard to contingency tables for chi-square tests for independence?

• Categorical rather than quantitative variables are being considered.

• Observed frequencies should be whole numbers

• Expected frequencies should be whole numbers.

• Expected frequencies in each cell should be at least 5, and to achieve this, one sometimes combines categories for one or the other or both of the variables.

• The expected frequency for any cell can be found by multiplying the row total by the column total and dividing by the sample size.