Sample data are randomly drawn from three independent populations, each of size 100. The sample proportions are p^1 = 40/100, p^2 = 30/100, and p3 = 20/100.
a. At the 0.05 significance level, test H0: p1 = p2.
b. At the 0.05 significance level, test H0: p2 = p3.
c. At the 0.05 significance level, test H0: p1 = p3.
d. In general, if hypothesis tests lead to the conclusions that p1 = p2 and p2 = p3 are reasonable, does it follow that p1 = p3 is also reasonable? Why or why not?