The standard error formula y = / n treats the population size as infinitely large relative to the sample size n. The formula for

The standard error formula σ¯y = σ/
√
n treats the population size as infinitely large relative to the sample size n. The formula for σ¯y for a finite population size denoted by N is

N-n Oy = VN-1 The term (N-n)/(N-1) is called the finite popula- tion correction. (a) When n 300 students are selected from a col- lege student body of size N = 30,000, show that = 0.9950/n. (In practice, n is usually small relative to N, so the correction has little influence.) (b) If n = N (i.e., we sample the entire population), show that y = 0. In other words, no sampling error occurs, be- cause y = . (c) For n = 1, explain why the sampling distribution of y and its standard error are identical to the population dis- tribution and its standard deviation.