Assume that you plan to use a significance level of $\alpha = 0.05$ test the claim that p $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ , Use the given sample sizes and
numbers of successes to find the pooled estimate $\overline { \mathrm { p } }$ . Round your answer to the nearest thousandth.
-$$\begin{aligned}
\mathrm { n } _ { 1 } & = 100 & \mathrm { n } _ { 2 } & = 100 \
\hat { \mathrm { p } } 1 & = 0.11 & \hat { \mathrm { p } } _ { 2 } & = 0.15
\end{aligned}$$
A) 0.361
B) 0.260
C) 0.163
D) 0.130

Question

Quizplus · Accepted Answer

The pooled estimate $\overline{p}$ is calculated as $\overline{p} = \frac{x_1 + x_2}{n_1 + n_2}$, where $x_1 = n_1 \cdot \hat{p}_1$ and $x_2 = n_2 \cdot \hat{p}_2$. Here, $x_1 = 100 \cdot 0.11 = 11$ and $x_2 = 100 \cdot 0.15 = 15$. Thus, $\overline{p} = \frac{11 + 15}{100 + 100} = \frac{26}{200} = 0.130$.

Assume That You Plan to Use a Significance Level Of \alpha