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.
-A report on the nightly news broadcast stated that 13 out of 103 households with pet dogs were burglarized and 23 out of 177 without pet dogs were burglarized.
A) $z = 0.000$
B) $z = - 0.153$
C) $z = - 0.036$
D) $\mathrm { z } = - 0.090$

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.
-A report on the nightly news broadcast stated that 13 out of 103 households with pet dogs were burglarized and 23 out of 177 without pet dogs were burglarized. 
A) $z = 0.000$
B) $z = - 0.153$
C) $z = - 0.036$
D) $\mathrm { z } = - 0.090$

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 $\hat{p}_1 = \frac{13}{103}$, $\hat{p}_2 = \frac{23}{177}$, and $\hat{p} = \frac{13+23}{103+177}$. Substituting these values gives $ z \approx -0.090 $.

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