Solve the Problem $\sigma _ { \mathrm { x } } = \frac { \sigma } { \sqrt { \mathrm { n } } } \sqrt { \frac { \mathrm { N } - \mathrm { n } } { \mathrm { N } - 1 } }$

Essay

Solve the problem.
-When sampling without replacement from a finite population of size N, the following formula is used to find
the standard deviation of the population of sample means: $\sigma _ { \mathrm { x } } = \frac { \sigma } { \sqrt { \mathrm { n } } } \sqrt { \frac { \mathrm { N } - \mathrm { n } } { \mathrm { N } - 1 } }$ However, when the sample size n, is smaller than 5% of the population size, N, the finite population correction
factor, $\sqrt { \frac { N - n } { N - 1 } }$ , can be omitted. Explain in your own words why this is reasonable. For N = 200, find the
values of the finite population correction factor when the sample size is 10%, 5%, 3%, 1% of the population,
respectively. What do you notice?