Construct and Interpret Confidence Intervals for the Difference between Two Population Proportions
-Construct a $95 \%$ confidence interval for $\mathrm { P } 1 - \mathrm { P } 2$. The sample statistics listed below are from independent samples.
Sample statistics: $\mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 1 } = 35$, and $\mathrm { n } _ { 2 } = 60 , \mathrm { x } _ { 2 } = 40$
A) $( - 0.141,0.208 )$
B) $( - 0.871,0.872 )$
C) $( - 1.341,1.781 )$
D) $( - 2.391,3.112 )$

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for $P_1 - P_2$, first calculate the sample proportions: $p_1 = \frac{x_1}{n_1} = \frac{35}{50} = 0.7$ and $p_2 = \frac{x_2}{n_2} = \frac{40}{60} = 0.6667$. Then, use the formula for the confidence interval of the difference between two proportions: $\hat{p}_1 - \hat{p}_2 \pm z \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$, where $z$ is the z-score for a 95% confidence level (approximately 1.96). Plugging in the values gives a confidence interval of $(-0.141, 0.208)$.

Construct and Interpret Confidence Intervals for the Difference Between Two 95%95 \%95%

Construct and Interpret Confidence Intervals for the Difference Between Two $95 \%$