Question

A vehicle quality survey asked new owners a variety of questions about their recently purchased automobile (JD. Power and Associates, March 2012). One question asked for the owner's rating of the vehicle using categorical responses of average, outstanding, and exceptional. Another question asked for the owner's education level with the categorical responses some high school, high school graduate, some college, and college graduate. Assume the sample data below are for 500 owners who had recently purchased an automobile.

a. Use a .05 level of significance and a test of independence to determine if a new owner's vehicle quality rating is independent of the owner's education. What is the p-value and what is your conclusion?
b. Use the overall percentage of average, outstanding, and exceptional ratings to comment on how new owners rate the quality of their recently purchased automobiles.

Answer 1

The question involves using a chi-square test to determine independence between vehicle quality rating and education level. A p-value less than 0.05 rejects the null hypothesis. The second part of the question cannot be addressed without the specific rating percentages.

Step-by-step explanation:

To determine if a new owner's vehicle quality rating is independent of the owner's education, we use a chi-square test of independence. Since the data is categorical, this statistical test is appropriate. We would need to create a contingency table of the observed frequencies of each combination of vehicle quality rating and education level, calculate the expected frequencies, and then compute the chi-square statistic. Comparing the calculated statistic to the chi-square distribution table for the respective degrees of freedom at a 0.05 level of significance would provide us with the p-value. If the p-value is below 0.05, we would reject the null hypothesis that vehicle quality rating is independent of education level.

For part b, we would need to know the overall percentage of average, outstanding, and exceptional ratings from the survey data to comment on how new owners rate their vehicles. Without this information, we cannot provide a conclusion on the vehicle ratings.