Construct a 95% confidence interval for $p _ { 1 } - p _ { 2 }$ Assume the samples are random and independent. Sample statistics: $\mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 1 } = 35 , \text { and } \mathrm { n } _ { 2 } = 60 , \mathrm { x } _ { 2 } = 40$
A)(-0.141, 0.208)
B)(-0.871, 0.872)
C)(-1.341, 1.781)
D)(-2.391, 3.112)

Question

Quizplus · Accepted Answer

The confidence interval for the difference between two proportions $p_1 - p_2$ is calculated using the formula: $$ \hat{p}_1 - \hat{p}_2 \pm Z \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}} $$ where $\hat{p}_1 = \frac{x_1}{n_1}$, $\hat{p}_2 = \frac{x_2}{n_2}$, and $Z$ is the Z-score corresponding to the desired confidence level (for 95% confidence, $Z \approx 1.96$). Given $n_1 = 50, x_1 = 35, n_2 = 60, x_2 = 40$, we find $\hat{p}_1 = 0.7$, $\hat{p}_2 = 0.6667$, and then calculate the interval, which results in (-0.141, 0.208).

Construct a 95% Confidence Interval For p1−p2p _ { 1 } - p _ { 2 }p1​−p2​

Construct a 95% Confidence Interval For $p _ { 1 } - p _ { 2 }$