A student who needs to pass an elementary statistics course wonders whether it will make a difference if she takes the course with instructor A rather than instructor B. Observing the final grades given by each instructor in a recent elementary statistics course, she finds that Instructor A gave 48 passing grades in a class of 52 students and Instructor B gave 44 passing grades in a class of 54 students. Assume that these classes and grades make simple random samples of all classes and grades of these instructors.
a. Compute the value of the standard normal test statistic z of Section 10.5.3 for the data and use it to find the p-value when testing for the difference between the proportions of passing grades given by these instructors.
b. Construct a 2 × 2 contingency table for these data. Compute the value of the 2 test statistic for the test of independence and use it to find the p-value.
c. How do the test statistics in parts a and b compare? How do the p-values for the tests in parts a and b compare? Do you think this is a coincidence, or do you think this will always happen?