Suppose that you sample two normal populations independently The variances of these two populations are 2 1 and 2 1 You take random samples of sizes n 1 , and n 2 , and observe sample variances of s 2 1 and s 2 2 a If n 1 n 2 , 2 1 , how large must the fraction s 1 s 2 , be before you can reject the null hypothesis that o 2 1 is no greater than o 2 2 at the 5 significance level b Answer part a when n 1 n 2 41 c If s 1 is 25 greater than s 2 , approximately how large must n 1 and n 2 , be if you are able to reject the null hypothesis in part a at the 5 significance level Assume that n 1 and n 2 are equal

Question: Suppose that you sample two normal populations independently. The variances of these two populations are 2 1 and 2 1 You take random

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.

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