Let S2 be the variance of a random sample of size n from N(μ, Ï2). Using the

Let S2 be the variance of a random sample of size n from N(μ, σ2). Using the fact that (n ˆ’ 1)S2/σ2 is χ2(nˆ’1), note that the probability

Where

Rewrite the inequalities to obtain

If n = 13 and

Show that [6.11, 24.57] is a 90% confidence interval for the variance σ2. Accordingly, [2.47, 4.96] is a 90% confidence interval for σ.

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a = χ2-a/2(n-1 ) and b = X2/2 (n-1 ). P (n-1)S2 < σ2 < (n-1)S2 = 1-α. 125-= Σ21 (xi-x)-= 128.41.