Question

For the population of N = 5 units of Exercise 3 of Chapter 2

(a) Compute directly the variance var (y) of the sample mean and the variance var( m ) of the sample median.

(b) From each sample, compute the sample variance s 2 and the estimate var (y) of the variance of the sample mean. Show that the sample variance s 2 is unbiased for the √ finite-population variance σ 2 but that the sample standard deviation 2 √ s = s is not unbiased for the population standard deviation σ 2 .

(c)each sample, construct a standard 95% confidence interval for the population mean. What is the actual coverage probability for the method with this population and design?

3. For the population of N 5 units of Exercise 3 of Chapter 2 (a) Compute directly the variance var() of the sample mean and the variance var(m) of the sample median. (b) From each sample, compute the sample variance s and the estimate var(y) of the variance of the sample mean. Show that the sample variance s2 is unbiased for the finite-population variance σ-but that the sample standard deviation ss2is not unbiased for the population standard deviation (c) For each sample, construct a standard 95% confidence interval for the population mean. What is the actual coverage probability for the method with this population and design?

below is ex3 of chapter2:

Answer 1