Question: Normal distribution N ( , 2 ) , Confidence intervals for z-score: y z 0.975 n S n 1 , for t-score: y t n

Normal distribution N(,2), Confidence intervals for z-score: yz0.975nSn1, for t-score: ytn1,0.975nSn1. For z-score (z0.975) and t-score (tn1,0.975), n = 10, 15, 20, 40, 100, 400. The estimate y is the observed value of the estimator Y. What is the expectation and variance of this estimator under the specified model? Use these formulas to explain why the sample mean is an unbiased and consistent estimator of the population mean.

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