For which of the following scenarios is a chi-square test of homogeneity appropriate?

Question

(A) A car manufacturer examines a random sample of 350 of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week.

(B) A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients, testing whether the cholesterol level (in milligrams) is related to whether or not a person has heart disease.

(C)A student wants to find out whether political party is related to choice of major. He surveys 500 randomly chosen students about their political party and their major to perform a test.

(D)A head of surgery is concerned that surgical residents in training apply unnecessary blood transfusions at a different rate than the more experienced attending physicians. She orders a study of the 49 Attending Physicians and 71 Residents in Training with privileges at the hospital and classifies them as occasionally, rarely, or never performing unnecessary blood transfusions to perform a test.

(E) None of the above.

Answer 1

Choice A: A chi-squared goodness-of-fit test would be appropriate to assess whether the defects are randomly distributed across days of the work week for the car manufacturer's warranty claims.

In the situation where the car manufacturer is examining defects across days of the workweek, a chi-squared goodness-of-fit test is appropriate. This test helps determine if observed frequencies (defects) match expected frequencies (random distribution) across different categories (days of the week).

Choice B: A chi-squared test of independence would be suitable to determine the relationship between blood cholesterol levels and the presence of heart disease among the medical researcher's database of patients.

For the medical researcher's investigation into the relationship between blood cholesterol levels and heart disease, a chi-squared test of independence is suitable. This test assesses whether there's a statistically significant association between two categorical variables (cholesterol level and presence of heart disease) within a contingency table.

Choice C: A chi-squared test of independence would be applicable to analyze the potential relationship between political leaning and choice of major among the surveyed students.

In the scenario involving the student's survey on political leaning and choice of major, a chi-squared test of independence is relevant. This test helps determine if there's a significant association between two categorical variables (political leaning and choice of major) and whether they are independent or related.

Choice D: A chi-squared test of homogeneity would be applicable to determine whether surgical residents or attending physicians share the same rate of blood transfusions.

In the scenario that involves how often each doctor performs blood transfusions at a specific rate, a chi-squared test of homogeneity is applicable. This test decide if two populations (attending physicians and surgical residents) with unknown distributions (rate of blood transfusions) have the same distribution as each other.

Choice D is the correct answer.