8.73 Find the power. Consider testing the null hypothesis that two proportions are equal versus the two-sided alternative with α = 0.05, 80% power, and equal sample sizes in the two groups.

1. (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.

2. (b) Write a short summary describing your results.