Ward's Communications reports the distribution of colors among sports car enthusiasts. A sample of 250 cars at a NASCAR raceway shows various colors. Which test assesses whether NASCAR color preferences are typical of sports car enthusiasts?

Ward's Communications reports the distribution of colors among sports car enthusiasts. A sample of 250 cars at a NASCAR raceway shows various colors. Which test assesses whether NASCAR color preferences are typical of sports car enthusiasts?

• A. Chi-square test of independence
• B. Linear regression
• C. Chi-square goodness of fit with 5 degrees of freedom
• D. 2-proportion z-test

Answer: (C)

This item tests whether observed color frequencies among NASCAR cars match the expected frequencies from sports car enthusiasts. When you have one categorical variable (color) with several categories and a hypothesized distribution for that variable, the appropriate method is a chi-square goodness-of-fit test. It compares what you actually observed to what you would expect if NASCAR color choices followed the same distribution reported for sports car enthusiasts (as provided by Ward’s Communications). You compute the expected counts by multiplying the total sample size by each category’s proportion from the sports car enthusiasts distribution, then sum (observed − expected)² divided by the expected for all categories. The test uses degrees of freedom equal to the number of color categories minus one; here that’s five, which matches the option describing a chi-square goodness-of-fit test with 5 degrees of freedom. If the resulting p-value is small, you conclude the NASCAR colors differ from the typical sports car enthusiast distribution; if not, you do not have evidence of a difference. The other tests aren’t appropriate here: a test of independence would be for two categorical variables, linear regression deals with relationships between variables, and a 2-proportion z-test compares two proportions rather than a full categorical distribution to a specified one.

This item tests whether observed color frequencies among NASCAR cars match the expected frequencies from sports car enthusiasts. When you have one categorical variable (color) with several categories and a hypothesized distribution for that variable, the appropriate method is a chi-square goodness-of-fit test. It compares what you actually observed to what you would expect if NASCAR color choices followed the same distribution reported for sports car enthusiasts (as provided by Ward’s Communications).

You compute the expected counts by multiplying the total sample size by each category’s proportion from the sports car enthusiasts distribution, then sum (observed − expected)² divided by the expected for all categories. The test uses degrees of freedom equal to the number of color categories minus one; here that’s five, which matches the option describing a chi-square goodness-of-fit test with 5 degrees of freedom.

If the resulting p-value is small, you conclude the NASCAR colors differ from the typical sports car enthusiast distribution; if not, you do not have evidence of a difference. The other tests aren’t appropriate here: a test of independence would be for two categorical variables, linear regression deals with relationships between variables, and a 2-proportion z-test compares two proportions rather than a full categorical distribution to a specified one.