Exam 15: The Chi-Square Statistic: Tests for Goodness of Fit and Independence

A researcher would like to test the claim that 9 out of 10 doctors prefer Brand X.A sample of 60 doctors is obtained and each is asked to compare Brand X with another leading brand.The data show that 48 of the doctors picked Brand X.If these data are evaluated using a chi-square test for goodness of fit,what is the expected frequency for Brand X?

Under what circumstances should the chi-square statistic not be used?

Which of the following accurately describes the observed frequencies for a chi-square test?

A chi-square test should not be used if any expected frequency is less than five.

The data for a chi-square test consist of ___________.

For a chi-square test for independence,the expected frequencies for any row are the same as the expected frequencies in every other row.

The observed frequencies for a chi-square test can be fractions or decimal values.

What is referred to by the term expected frequencies?

A chi-square test for goodness of fit has df = 2.How many categories were used to classify the individuals in the sample?

Under what circumstances will the chi-square test for goodness of fit produce a large value for the chi-square?

Chi-square values are always greater than or equal to zero.

In general,a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

What is stated by the null hypothesis for the chi-square test for independence?

The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

Which of the following is always true for a chi-square test for goodness of fit or a test for independence?

A large value for the chi-square statistic indicates a large discrepancy between the sample data and the hypothesis.

What is referred to by the term observed frequencies?

The chi-square distribution tends to be symmetrical with a mean of μ = 0.

What happens to the shape of the chi-square distribution as the df value increases?

A researcher selects a sample of 100 people to investigate the relationship between gender (male/female)and registering to vote.The sample consists of 40 females,of whom 30 are registered voters,and 60 males,of whom 40 are registered voters.If these data were used for a chi-square test for independence,what is the expected frequency for registered females?