Suppose that you sample two normal populations inde- pendently. The variances of these two populations are oj and ož. You take random samples of sizes n, and n and observe sample variances of sĩ and sz. a. If n¡ = n2 = 21, how large must the fraction s1/s2 be before you can reject the null hypothesis that of is no greater than ơž at the 5% significance level? b. Answer part a when n¡ = n, = 41. c. If s¡ is 25% greater than s2, approximately how large must n¡ and n, be if you are able to reject the null hypothesis in part a at the 5% significance level? Assume that n¡ and nɔ are equal.

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Suppose that you sample two normal populations inde-
pendently. The variances of these two populations are
of and ož. You take random samples of sizes n¡ and n2
and observe sample variances of s¡ and sz.
a. If n¡ = n2 = 21, how large must the fraction s1/s2 be
before you can reject the null hypothesis that of is no
greater than ơ at the 5% significance level?
b. Answer part a when n¡ = n, = 41.
c. If s, is 25% greater than s2, approximately how large
must n¡ and nɔ be if you are able to reject the null
hypothesis in part a at the 5% significance level?
Assume that n¡ and nɔ are equal.
Transcribed Image Text:Suppose that you sample two normal populations inde- pendently. The variances of these two populations are of and ož. You take random samples of sizes n¡ and n2 and observe sample variances of s¡ and sz. a. If n¡ = n2 = 21, how large must the fraction s1/s2 be before you can reject the null hypothesis that of is no greater than ơ at the 5% significance level? b. Answer part a when n¡ = n, = 41. c. If s, is 25% greater than s2, approximately how large must n¡ and nɔ be if you are able to reject the null hypothesis in part a at the 5% significance level? Assume that n¡ and nɔ are equal.
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