Transitivity of Hypothesis Tests Sample data are randomly drawn from three independent populations, each of size 100. The sample proportions are 1 5 40 100, 2 5 30 100, and 3 5 20 100.

a. At the 0.05 significance level, test H0: p1 5 p2.

b. At the 0.05 significance level, test H0: p2 5 p3.

c. At the 0.05 significance level, test H0: p1 5 p3.

d. In general, if hypothesis tests lead to the conclusions that p1 5 p2 and p2 5 p3 are reasonable, does it follow that p1 5 p3 is also reasonable? Why or why not?