The table shows the number of households burglarized in a sample of households with dogs and in a sample of households without dogs. Assume that you plan to use a significance level of $\alpha = 0.01$ to test the claim that $\mathrm { p } _ { 1 }

Question

The table shows the number of households burglarized in a sample of households with dogs and in a sample of households without dogs. Assume that you plan to use a significance level of $\alpha = 0.01$ to test the claim that $\mathrm { p } _ { 1 } < \mathrm { p } _ { 2 }$. Find the critical value(s) for this hypothesis test. Do the data support the claim that a smaller proportion of households with pet dogs are burglarized?
$\begin{array}{lcc}
\hline & \text { Household with Dog } & \text { Household without Dog } \
\hline \text { Number of households in sample } & 225 & 137 \
\text { Number of households burglarized } & 25 & 10 \
\hline
\end{array}$
A) $\mathrm { z } = - 2.575$; no
B) $z = - 2.33$; no
C) $z = - 1.96$; yes
D) $z = 2.33$; yes

Quizplus · Accepted Answer

The critical value for a left-tailed test at $\alpha = 0.01$ is $z = -2.33$. Since the test statistic is not less than $-2.33$, the data do not support the claim.

The Table Shows the Number of Households Burglarized in a Sample