11-45. Confidence Interval for a Population Total:

Let {X1, . . . ,Xn} constitute a set of sample random variables taken from a population of sizeN.Weare interested in determining an interval estimate for the population total τ = Nj

=1 Xj . Let NX serve as an estimator for

τ . Then for N¯x the sample realization of NX, a 100(1 − α)% confidence interval for τ is N¯x ± zα/2

?51 − n N

6 (Ns)2 n

, where s is the realized sample standard deviation. Suppose that from a random sample of size n = 50 taken from a population of size N = 750 it is found that ¯x = 81.2 and s = 9.8. Find a 90% confidence interval for the population total.