Assume that you plan to use a significance level of $\alpha = 0.05$ test the claim that p $\mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
-In a vote on the Clean Water bill, 46% of the 205 Democrats voted for the bill while 48% of the 230 Republicans voted for it.
A) z = -0.417
B) z = -0.250
C) z = -0.459
D) z = -0.354

Question

Quizplus · Accepted Answer

The z test statistic for the hypothesis test is:$$z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}$$where $\hat{p}_1$ and $\hat{p}_2$ are the sample proportions, $\hat{p}$ is the pooled proportion, and $n_1$ and $n_2$ are the sample sizes.In this case, we have:$$\hat{p}_1 = 0.46$$$$\hat{p}_2 = 0.48$$$$\hat{p} = \frac{0.46(205) + 0.48(230)}{205 + 230} = 0.47$$$$n_1 = 205$$$$n_2 = 230$$Plugging these values into the formula, we get:$$z = \frac{0.46 - 0.48}{\sqrt{0.47(1-0.47)(\frac{1}{205}+\frac{1}{230})}} = -0.417$$Therefore, the correct answer is A.

Assume That You Plan to Use a Significance Level Of \alpha