Suppose that you sample two normal populations independently. The variances of these two populations are 2

Suppose that you sample two normal populations independently. The variances of these two populations are σ²₁ and σ²₁ You take random samples of sizes n₁, and n₂, and observe sample variances of s²₁ and s²₂.

a. If n₁ = n₂, = 2₁, how large must the fraction s₁/s₂, be before you can reject the null hypothesis that o²₁ is no greater than o²₂ at the 5% significance level?

b. Answer part a when n₁ = n₂ = 41.

c. If s₁ is 25% greater than s₂, approximately how large must n₁ and n₂, be if you are able to reject the null hypothesis in part a at the 5% significance level? Assume that n₁ and n₂ are equal.