Assume that you plan to use a significance level of $\alpha = 0.05$ to test the claim that $p _ { 1 } = p _ { 2 }$. Use the given sample sizes and numbers of successes to find the pooled estimate $\bar { p }$. Round your answer to the nearest thousandth.
$\begin{array} { l l }
n _ { 1 } = 677 & n _ { 2 } = 3377 \
x _ { 1 } = 172 & x _ { 2 } = 654
\end{array}$
A) $0.163$
B) $0.452$
C) $0.204$
D) $0.408$

Question

Assume that you plan to use a significance level of $\alpha = 0.05$ to test the claim that $p _ { 1 } = p _ { 2 }$. Use the given sample sizes and numbers of successes to find the pooled estimate $\bar { p }$. Round your answer to the nearest thousandth.
$\begin{array} { l l } 
n _ { 1 } = 677 & n _ { 2 } = 3377 \
x _ { 1 } = 172 & x _ { 2 } = 654
\end{array}$
A) $0.163$
B) $0.452$
C) $0.204$
D) $0.408$

Quizplus · Accepted Answer

The pooled estimate of the proportion is given by:$$\bar{p} = \frac{x_1 + x_2}{n_1 + n_2}$$Plugging in the given values, we get:$$\bar{p} = \frac{172 + 654}{677 + 3377} = 0.204$$Therefore, the pooled estimate of the proportion is 0.204, which is rounded to the nearest thousandth.

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