With a random sample of 800 adults, attitudes toward cloning laws are categorized by education level (high school, 2-year college, 4-year college, or advanced degree). To test whether cloning opinions are associated with education level, which test should be used?

With a random sample of 800 adults, attitudes toward cloning laws are categorized by education level (high school, 2-year college, 4-year college, or advanced degree). To test whether cloning opinions are associated with education level, which test should be used?

• A. Fisher's exact test
• B. T-test for independence
• C. Chi-square goodness of fit with 3 degrees of freedom
• D. Chi-square test of independence with 6 degrees of freedom

Answer: (D)

This question is about whether two categorical variables are related: education level and attitude toward cloning laws. When both variables are categorical, the chi-square test of independence is the standard method to assess if the distribution of one variable differs across the categories of the other. Think of the data in a contingency table: education level has four categories, and attitude has three categories (for example, in favor, neutral, against). The test uses degrees of freedom calculated as (rows − 1) × (columns − 1). Here that’s (4 − 1) × (3 − 1) = 3 × 2 = 6, so the appropriate test is the chi-square test of independence with six degrees of freedom. Fisher’s exact test is typically reserved for small samples or 2×2 tables and isn’t the standard choice for a larger, multi-category table. A t-test for independence is for comparing means of a continuous variable across groups, not for two categorical variables. A chi-square goodness of fit test checks whether a single categorical variable follows a specified distribution, not whether two variables are related. So the correct approach is the chi-square test of independence with six degrees of freedom.

This question is about whether two categorical variables are related: education level and attitude toward cloning laws. When both variables are categorical, the chi-square test of independence is the standard method to assess if the distribution of one variable differs across the categories of the other.

Think of the data in a contingency table: education level has four categories, and attitude has three categories (for example, in favor, neutral, against). The test uses degrees of freedom calculated as (rows − 1) × (columns − 1). Here that’s (4 − 1) × (3 − 1) = 3 × 2 = 6, so the appropriate test is the chi-square test of independence with six degrees of freedom.

Fisher’s exact test is typically reserved for small samples or 2×2 tables and isn’t the standard choice for a larger, multi-category table. A t-test for independence is for comparing means of a continuous variable across groups, not for two categorical variables. A chi-square goodness of fit test checks whether a single categorical variable follows a specified distribution, not whether two variables are related.

So the correct approach is the chi-square test of independence with six degrees of freedom.