The Table Shows the Number of Households Burglarized in a Sample

Multiple Choice

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