Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
-$$\begin{array} { l l }
\mathrm { n } _ { 1 } = 124 & \mathrm { n } _ { 2 } = 119 \
\mathrm { x } _ { 1 } = 51 & \mathrm { x } _ { 2 } = 43
\end{array}$$
A) $z = 8.951$
B) $z = 0.799$
C) $z = 0.395$
D) $\mathrm { z } = 16.623$

Question

Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ . Use the given sample sizes and
numbers of successes to find the z test statistic for the hypothesis test.
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 124 & \mathrm { n } _ { 2 } = 119 \
\mathrm { x } _ { 1 } = 51 & \mathrm { x } _ { 2 } = 43
\end{array}$$
A) $z = 8.951$
B) $z = 0.799$
C) $z = 0.395$
D) $\mathrm { z } = 16.623$

Quizplus · Accepted Answer

The z test statistic is calculated using the formula for 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 values gives $z \approx 0.799$.

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