# Question

A researcher claims that she can reduce the variance of N(μ,100) by a new manufacturing process. If S2 is the variance of a random sample of size n from this new distribution, she tests H0: σ2 = 100 against H1: σ2 < 100 by rejecting H0 if (n − 1)S2/100 ≤ χ1−α(n − 1) since (n − 1)S2/100 is χ2(n − 1) when H0 is true.

(a) If n = 23, S2 = 32.52, and α = 0.025, would she reject H0?

(b) Based on the same distributional result, what would be a reasonable test of H0: σ2 = 100 against a two sided alternative hypothesis H1: σ2 ≠ 100 when α = 0.05?

(a) If n = 23, S2 = 32.52, and α = 0.025, would she reject H0?

(b) Based on the same distributional result, what would be a reasonable test of H0: σ2 = 100 against a two sided alternative hypothesis H1: σ2 ≠ 100 when α = 0.05?

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