Find the standardized test statistic, z to test the claim that $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ Assume the samples are random and independent.
Sample statistics: $\mathrm { n } _ { 1 } = 50 , \mathrm { x } _ { 1 } = 35 , \text { and } \mathrm { n } _ { 2 } = 60 , \mathrm { x } _ { 2 } = 40$
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, z, 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 $\hat{p}$ is the pooled proportion, calculated as:$$\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$$Plugging in the given values, we get:$$\hat{p} = \frac{35 + 40}{50 + 60} = 0.375$$$$z = \frac{0.35 - 0.40}{\sqrt{0.375(1-0.375)(\frac{1}{50}+\frac{1}{60})}} = 0.374$$

Find the Standardized Test Statistic, Z to Test the Claim p1=p2\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }p1​=p2​

Find the Standardized Test Statistic, Z to Test the Claim $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$