8.51 Find the power. Consider testing the null hypothesis that two proportions are equal versus the twosided alternative with =0.05 , 80% power, and equal

8.51 Find the power. Consider testing the null hypothesis that two proportions are equal versus the twosided alternative with

α=0.05 , 80% power, and equal sample sizes in the two groups.

a. For each of the following situations, find the required sample size: (i)

p1=0.1 and p2=0.2 , (ii)

p1=0.2 and p2=0.3 , (iii)

p1=0.3 and p2=0.4 , (iv)

p1=0.4 and p2=0.5 , (v)

p1=0.5 and p2=0.6 , (vi)

p1=0.6 and p2=0.7 , (vii)

p1=0.7 and p2=0.8 , and (viii)

p1=0.8 and p2=0.9 .

b. Write a short summary describing your results.