Refer to Exercise 2.

a. Find the probability that the proportion of graduates who pass the test is at most 0.20 higher than the proportion of dropouts who pass, assuming that the researcher’s report is correct.

b. Suppose that the difference (Graduate – Dropout) in the sample proportions who pass the test is exactly 0.20. Based on your result in part (a), would this give you reason to doubt the researcher’s claim? Explain your reasoning.

Exercise 2.

A researcher reports that 80% of high school graduates, but only 40% of high school dropouts, would pass a basic literacy test.5 Assume that the researcher’s claim is true. Suppose we give a basic literacy test to a random sample of 60 high school graduates and a separate random sample of 75 high school dropouts. Let p^G and p^D be the sample proportions of graduates and dropouts, respectively, who pass the test.