The formula Ï/n for the standard deviation of x actually is an approximation that treats the population

The formula σ/ˆšn for the standard deviation of x actually is an approximation that treats the population size as infinitely large relative to the sample size n. The exact formula for a finite population size N is

The term ˆš(N - n)/(N - 1) is called the finite population correction.
a. When n = 300 students are selected from a college student body of size N = 30,000, show that the standard deviation equals 0.995 σ/ˆšn. (When n is small compared to the population size N, the approximate formula works very well.)

b. If n = N (that is, we sample the entire population), show that the standard deviation equals 0. In other words, no sampling error occurs, since xÌ… = m in that case.

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N — по N – 1 Vn Standard deviation п