In a test for the difference between two proportions, the sample sizes were $n _ { 1 } = 84$ and $n _ { 2 } = 102$ and the numbers of events were $x _ { 1 } = 35 \text { and } x _ { 2 } = 64$ A test is made of the hypothesis $H _ { 0 } : p _ { 1 } = p _ { 2 } \text { versus } H _ { 1 } : p _ { 1 } \neq p _ { 2 }$
Compute the value of the test statistic.
A) -2.87
B) -2.80
C) -2.93
D) -2.70

Question

In a test for the difference between two proportions, the sample sizes were $n _ { 1 } = 84$ and $n _ { 2 } = 102$ and the numbers of events were $x _ { 1 } = 35 \text { and } x _ { 2 } = 64$ A test is made of the hypothesis $H _ { 0 } : p _ { 1 } = p _ { 2 } \text { versus } H _ { 1 } : p _ { 1 } \neq p _ { 2 }$
Compute the value of the test statistic.
A)  -2.87 
B)  -2.80 
C)  -2.93 
D)  -2.70

Quizplus · Accepted Answer

The test statistic for the difference between two proportions is:$$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}$$where $\hat{p}$ is the pooled proportion:$$\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$$Plugging in the values from the question, we get:$$\hat{p} = \frac{35 + 64}{84 + 102} = 0.485$$$$z = \frac{0.417 - 0.627}{\sqrt{0.485(1-0.485)(\frac{1}{84}+\frac{1}{102})}} = -2.87$$Therefore, the value of the test statistic is -2.87.

In a Test for the Difference Between Two Proportions, the Sample