A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 90% confident that the sample
Proportion will not differ from the true proportion by more than 5%?

Question

Quizplus · Accepted Answer

The sample size needed for estimating a population proportion with a specific confidence level and margin of error can be calculated using the formula: $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), $p$ is the estimated proportion (0.5 used for maximum sample size), and $E$ is the margin of error (0.05 for 5%). Plugging these values in gives $n = \frac{1.645^2 \times 0.5 \times (1-0.5)}{0.05^2} = 271$.

A Researcher at a Major Hospital Wishes to Estimate the Proportion