Let X 1 ,X 2 , . . .,X n be a random sample from N(,

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Let X1,X2, . . .,Xn be a random sample from N(μ, σ2), where both parameters μ and σ2 are unknown. A confidence interval for σ2 can be found as follows. We know that (n − 1)S22 is a random variable with a χ2(n − 1) distribution. Thus we can find constants a and b so that P((n − 1)S22 < b) = 0.975 and P(a < (n − 1)S22 < b) = 0.95.

(a) Show that this second probability statement can be written as

(b) If n = 9 and s2 = 7.93, find a 95% confidence interval for σ2.

(c) If μ is known, how would you modify the preceding procedure for finding a confidence interval for σ2?

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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