4.57. The standard error formula ay = a/Jn treats the population size N as infinitely large relative to the sample size n. The formula for ay for a finite population size N is IN - n (

^ v W - 1 y Vrc J The term yj{N - n)/[N - 1) is called the finite population correction.

(a) When n = 300 students are selected from a college student body ofsize N = 30,000, show that ay = 0.995(r/ (In practice, n is usually small relative to N, so the correction has little influence.)

(b) If n = iV (i.e., we sample the entire population), show that ay = 0. In other words, no sampling error occurs, because y = p..

(c) For « = 1, explain why the sampling distribution of y and its standard error arc identical to the population distribution and its standard deviation.