Question: A random sample X 1 , X 2 , X 3 , . . ., X 36 is given from a normal distribution with unknown

A random sample X₁, X₂, X₃, . . ., X₃₆ is given from a normal distribution with unknown mean μ = EX_i and unknown variance Var(X_i) = σ². For the observed sample, the sample mean is X̅ = 35.8, and the sample variance is S² = 12.5.

a. Find and compare 90%, 95%, and 99% confidence interval for μ.

b. Find and compare 90%, 95%, and 99% confidence interval for σ².

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