Chapter 7.1, Problem 39BB

Finite Population Correction Factor For Formulas 7-2 and 7-3 we assume that the population is infinite or very large and that we are sampling with replacement. When we sample without replacement from a relatively small population with size N, we modify E to include the finite population correction factor shown here, and we can solve for n to obtain the result given here. Use this result to repeat part (b) of Exercise 38, assuming that we limit our population to a county with 2500 women who have completed the time during which they can give birth.

${\text{E = z}}_{\text{α}/2}\sqrt{\frac{\hat{\text{p}}\hat{\text{q}}}{\text{n}}}\sqrt{\frac{\text{N}-\text{n}}{\text{N}-1}}$ $\text{n =}\frac{\text{N}\hat{\text{p}}\hat{\text{q}}{\left[{\text{z}}_{\text{α}/2}\right]}^2}{\hat{\text{p}}\hat{\text{q}}{\left[{\text{z}}_{\text{α}/2}\right]}^2\text{ + }\left(\text{N}-1\right){\text{E}}^2}$