5 A random sample from a normal population with unknown mean and variance 2 yields the following summary statistics n 25, X 28 6, S 5 0 (a) Find a 95 confidence interval for 2 and a 95 confidence interval for (b) Find 95 one sided lower and upper confidence limits for , and compare these limits with the limits you found in the two sided 95 confidence interval for Comment on why these limits are different

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Question: 5. A random sample from a normal population with unknown mean and variance 2 yields the following summary statistics: n = 25, X =

5. A random sample from a normal population with unknown mean μ and variance σ2 yields the following summary statistics: n = 25, ¯X = 28.6, S = 5.0

(a) Find a 95% confidence interval for σ2 and a 95% confidence interval for σ.

(b) Find 95% one-sided lower and upper confidence limits for σ, and compare these limits with the limits you found in the two-sided 95% confidence interval for σ.

Comment on why these limits are different.

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