Provide an appropriate response.
-Find the standardized test statistic, $\mathrm { z }$, to test the hypothesis that $\mathrm { p } 1

Question

Provide an appropriate response.
-Find the standardized test statistic, $\mathrm { z }$, to test the hypothesis that $\mathrm { p } 1 < \mathrm { p } 2$. Use $\alpha = 0.10$. The sample statistics listed below are from independent samples.
Sample statistics: $\mathrm { n } _ { 1 } = 550 , \mathrm { x } _ { 1 } = 121$, and $\mathrm { n } _ { 2 } = 690 , \mathrm { x } _ { 2 } = 195$
A) $- 2.513$
B) $- 2.132$
C) $- 0.985$
D) $1.116$

Quizplus · Accepted Answer

The standardized test statistic $ z $ is calculated using the formula for comparing two proportions: $$ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{\hat{p}(1 - \hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}} $$ 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, $\hat{p}_1 = \frac{121}{550}$, $\hat{p}_2 = \frac{195}{690}$, and $\hat{p} = \frac{121 + 195}{550 + 690}$, the calculation yields a $ z $-score of approximately $-2.513$, indicating that the test statistic for comparing the two proportions falls under choice A.

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

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