Construct and Interpret Confidence Intervals for the Difference between Two Population Proportions
-In a recent survey of drinking laws, a random sample of 1000 women showed that $65 \%$ were in favor of increasing the legal drinking age. In a random sample of 1000 men, $60 \%$ favored increasing the legal drinking age. Construct a $95 \%$ confidence interval for $\mathrm { P } 1$ - $\mathrm { p } 2$.
A) $( 0.008,0.092 )$
B) $( 0.587,0.912 )$
C) $( - 1.423,1.432 )$
D) $( - 2.153,1.679 )$

Question

Quizplus · Accepted Answer

The confidence interval for the difference between two population proportions is calculated using the formula: $$CI = (\hat{p}_1 - \hat{p}_2) \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$$ where $\hat{p}_1 = 0.65$, $\hat{p}_2 = 0.60$, $n_1 = n_2 = 1000$, and $Z_{\alpha/2}$ for a 95% confidence level is approximately 1.96. Plugging these values into the formula gives a confidence interval of approximately $(0.008, 0.092)$.

Construct and Interpret Confidence Intervals for the Difference Between Two 65%65 \%65%

Construct and Interpret Confidence Intervals for the Difference Between Two $65 \%$