Question

A recent study indicated that 38 % of the 89 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions.

Part 1 out of 2

How large a sample must you take to be 95 % confident that the estimate is within 0.04 of the true proportion of women over age 55 who are widows?

Answer 1

SOLUTION:

From given data,

$\hat{p}$ = 38% = 38/100 = 0.38

Confidence interval is 95%

95% = 95/100 = 0.95

$\alpha$ = 1 - Confidence interval = 1-0.95 = 0.05

$\alpha$/2 = 0.05 / 2

= 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

Sample size = n = (Z_$\alpha$/2 /E)^2 * $\hat{p}$ *(1-$\hat{p}$)

n = (1.96 /0.04)^2 * 0.38*(1-0.38)

n = (1.96 /0.04)^2 * 0.38*0.62​​​​

n = 2401 * 0.38*0.62​​​​

n = 565.6756

n = 566