Question

a political pollster selects a random sample of 75 registered voters from allegheny county, pennsylvania. the city of pittsburgh is in allegheny county. the pollster is interested in determining if the distribution of political party preference among registered voters in this county differs between those who live in pittsburgh and those who live in the suburbs. the responses are displayed in the table.

the pollster would like to know if these data provide convincing evidence of a relationship between residential status and political party in the population of all registered voters in allegheny county. what is the appropriate inference procedure?
chi - square test for goodness of fit because the data come from one random sample
chi - square test for homogeneity because the data come from one random sample
chi - square test for homogeneity because the data come from independent random samples
chi - square test for association/independence because the data come from one random sample
chi - square test for association/independence because the data come from independent random samples

Explanation:

• Chi - square test for goodness of fit: Compares observed frequencies to expected frequencies for a single categorical variable. Here, we have two categorical variables (residential status and political party), so this is not appropriate.
• Chi - square test for homogeneity: Compares distributions of a categorical variable across multiple independent samples. But we are interested in the relationship between two variables, not just comparing distributions of one variable across groups.
• Chi - square test for association/independence: Used to determine if there is a relationship between two categorical variables. When the data comes from one random sample (as in this case, one sample of 75 voters with two categorical variables - location (city/suburbs) and political party), this is the correct test.

Answer:

chi - square test for association/independence because the data come from one random sample.