11-14. If the population mean is to be estimated by a 100(1 )% confidence interval...

11-14. If the population mean μ is to be estimated by a 100(1 − α)% confidence interval and we are sampling without replacement from a finite population and n/N > 0.05, then a measure of how precisely we have estimated

μ is provided by ± error bound, where the error bound is w

2

= zα/2

√σ

n

?N − n N − 1

.

Solving this expression for n renders n = mN m + N − 1 , where m = 5zα/2σ
w/2 6 2 .
What is the interpretation of n? Suppose X is N(μ, 20) and the population size is N = 2300. How large of a sample is needed so that the 95%
confidence interval for the mean does not exceed 4 units in width?