Questions: Widows A recent study indicated that 18% of the 196 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions.
How large a sample must you take to be 90% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows?
n=
Transcript text: Widows A recent study indicated that $18 \%$ of the 196 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions.
Part: $0 / 2$ $\square$
Part 1 of 2
How large a sample must you take to be $90 \%$ confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows?
\[
n=
\]
$\square$
Solution
Solution Steps
Step 1: Given Information
We are tasked with determining the required sample size \( n \) to estimate the proportion of women over age 55 who are widows with a confidence level of \( 90\% \). The following values are provided:
Estimated proportion \( p = 0.18 \)
Margin of error \( E = 0.05 \)
Z-score for \( 90\% \) confidence level \( Z \approx 1.645 \)
Step 2: Sample Size Formula
The formula for calculating the required sample size \( n \) for estimating a population proportion is given by: