Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a $95 \%$ confidence interval for the true percentage of all adults that have high blood pressure.
A) $18.1 \%

Question

Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a $95 \%$ confidence interval for the true percentage of all adults that have high blood pressure.
A) $18.1 \% < p < 39.6 \%$
B) $21.9 \% < p < 35.7 \%$
C) $19.1 \% < p < 38.5 \%$
D) $20.6 \% < p < 37.0 \%$

Quizplus · Accepted Answer

The sample proportion is $ \hat{p} = \frac{34}{118} \approx 0.2881 $. Using the formula for a confidence interval for a proportion, $ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $, with $ Z \approx 1.96 $ for a 95% confidence level, the interval is approximately $ 0.206 < p < 0.370 $, which corresponds to $ 20.6\% < p < 37.0\% $.

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Of 118 Randomly Selected Adults, 34 Were Found to Have $95 \%$