Provide an appropriate response.
-Find the standardized test statistic, $\mathrm { z }$, to test the hypothesis that $\mathrm { p } 1 \neq \mathrm { p } _ { 2 }$. Use $\alpha = 0.02$. The sample statistics listed below are from independent samples.
Sample statistics: $\mathrm { n } _ { 1 } = 1000 , \mathrm { x } _ { 1 } = 250$, and $\mathrm { n } _ { 2 } = 1200 , \mathrm { x } _ { 2 } = 195$
A) $5.087$
B) $2.798$
C) $4.761$
D) $3.212$

Question

Quizplus · Accepted Answer

The standardized test statistic $ z $ is calculated using the formula for comparing two proportions: $$ z = \frac{ \hat{p}_1 - \hat{p}_2 }{ \sqrt{ \hat{p}(1 - \hat{p}) \left( \frac{1}{n_1} + \frac{1}{n_2} \right) } } $$ where $\hat{p}_1 = \frac{x_1}{n_1}$, $\hat{p}_2 = \frac{x_2}{n_2}$, and $\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$. Plugging in the given values: $\hat{p}_1 = \frac{250}{1000} = 0.25$, $\hat{p}_2 = \frac{195}{1200} = 0.1625$, and $\hat{p} = \frac{250 + 195}{1000 + 1200} = \frac{445}{2200} = 0.2023$. Substituting these into the formula gives a $ z $ value of approximately $5.087$.

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

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