Suppose that you sample two normal populations independently. The variances of these two populations are σ12 and σ22. You take random samples of sizes n1and n2 and observe sample variances of s12 and s22. a. If n1 = n2 = 21, how large must the fraction s1/s2 be before you can reject the null hypothesis that σ12 is no greater than σ22 at the 5% significance level? Round your answer to two decimal places, if necessary. The ratio must at least to reject the null hypothesis. b. If n1 = n2 = 41, how large must the fraction s1/s2 be before you can reject the null hypothesis that σ12 is no greater than σ22 at the 5% significance level? Round your answer to two decimal places, if necessary. The ratio must be at least to reject the null hypothesis. 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. The sample sizes must be at least to reject the null hypothesis.
Suppose that you sample two normal populations independently. The variances of these two populations are σ12 and σ22. You take random samples of sizes n1and n2 and observe sample variances of s12 and s22.
a. If n1 = n2 = 21, how large must the fraction s1/s2 be before you can reject the null hypothesis that σ12 is no greater than σ22 at the 5% significance level? Round your answer to two decimal places, if necessary.
The ratio must at least to reject the null hypothesis.
b. If n1 = n2 = 41, how large must the fraction s1/s2 be before you can reject the null hypothesis that σ12 is no greater than σ22 at the 5% significance level? Round your answer to two decimal places, if necessary.
The ratio must be at least to reject the null hypothesis.
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.
The sample sizes must be at least to reject the null hypothesis.
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