Provide an appropriate response.
-Find the standardized test statistic, $\mathrm { z }$ to test the hypothesis that $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$. Use $\alpha = 0.05$. 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) $0.374$
B) $0.982$
C) $1.328$
D) $2.361$

Question

Quizplus · Accepted Answer

The correct answer is A because the standardized test statistic is calculated as:$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}}$where $\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$ is the pooled proportion.Plugging in the given values, we get:$\hat{p} = \frac{35 + 40}{50 + 60} = 0.375$$z = \frac{0.35 - 0.40}{\sqrt{0.375(1-0.375)(\frac{1}{50} + \frac{1}{60})}} = 0.374$

Provide an Appropriate Response z\mathrm { z }z To Test the Hypothesis That

Provide an Appropriate Response $\mathrm { z }$ To Test the Hypothesis That