Find a 95% confidence interval for the true population proportion.
-In a poll of 1810 adults, 33% said that they exercised regularly.
A) $28.3 \%$ to $37.7 \%$
B) $32.9 \%$ to $33.1 \%$
C) $31.8 \%$ to $34.2 \%$
D) $30.6 \%$ to $35.4 \%$

Question

Find a 95% confidence interval for the true population proportion.
-In a poll of 1810 adults, 33% said that they exercised regularly. 
A) $28.3 \%$ to $37.7 \%$
B) $32.9 \%$ to $33.1 \%$
C) $31.8 \%$ to $34.2 \%$
D) $30.6 \%$ to $35.4 \%$

Quizplus · Accepted Answer

The confidence interval for a proportion is calculated using the formula: $\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $Z$ is the Z-score for the confidence level, and $n$ is the sample size. For a 95% confidence level, $Z$ is approximately 1.96. Here, $\hat{p} = 0.33$ and $n = 1810$. Calculating gives the interval $30.6\%$ to $35.4\%$.

Find a 95% Confidence Interval for the True Population Proportion 28.3%28.3 \%28.3%

Find a 95% Confidence Interval for the True Population Proportion $28.3 \%$