Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ , Use the given sample sizes and
numbers of successes to find the pooled estimate $\overline { \mathbf { p } }$ . Round your answer to the nearest thousandth.
-$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \
\hat { \mathrm { p } } = 0.19 & \hat { \mathrm { p } _ { 2 } } = 0.16
\end{array}$$
A) 0.219
B) 0.350
C) 0.418
D) 0.175

Question

Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ , Use the given sample sizes and
numbers of successes to find the pooled estimate $\overline { \mathbf { p } }$ . Round your answer to the nearest thousandth.
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 100 \
\hat { \mathrm { p } } = 0.19 & \hat { \mathrm { p } _ { 2 } } = 0.16
\end{array}$$
A) 0.219
B) 0.350
C) 0.418
D) 0.175

Quizplus · Accepted Answer

The pooled estimate $\overline{p}$ is calculated as $\overline{p} = \frac{x_1 + x_2}{n_1 + n_2}$, where $x_1 = n_1 \times \hat{p}_1$ and $x_2 = n_2 \times \hat{p}_2$. Here, $x_1 = 100 \times 0.19 = 19$ and $x_2 = 100 \times 0.16 = 16$. Thus, $\overline{p} = \frac{19 + 16}{100 + 100} = \frac{35}{200} = 0.175$.

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