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) $21.9 \%

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) $21.9 \% < p < 35.7 \%$
B) $18.1 \% < p < 39.6 \%$
C) $19.1 \% < p < 38.5 \%$
D) $20.6 \% < p < 37.0 \%$

Quizplus · Accepted Answer

The sample proportion is 34/118 = 0.288. Using the formula for a confidence interval for a proportion, the interval is calculated as $ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $, where $ Z $ is the Z-score for 95% confidence (approximately 1.96). This results in the interval $ 0.206 < p < 0.370 $, which corresponds to choice D.

Of 118 Randomly Selected Adults, 34 Were Found to Have 21.9%<p<35.7%21.9 \% < p < 35.7 \%21.9%<p<35.7%

Of 118 Randomly Selected Adults, 34 Were Found to Have $21.9 \% < p < 35.7 \%$