A report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized. Assume that you plan to test the claim that p1=p2. Find the test statistic for the hypothesis test. (Let the houses with the dogs be the first population.)

We are given that a report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized.

Let [tex]p_1[/tex] = population proportion of households with pet dogs who were burglarized.

[tex]p_2[/tex] = population proportion of households without pet dogs who were burglarized.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex] {means that both population proportions are equal}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex] {means that both population proportions are not equal}

The test statistics that would be used here Two-sample z-test for proportions;

T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of households with pet dogs who were burglarized = [tex]\frac{10}{129}[/tex] = 0.08

[tex]\hat p_2[/tex] = sample proportion of households without pet dogs who were burglarized = [tex]\frac{23}{197}[/tex] = 0.12

[tex]n_1[/tex] = sample of households with pet dogs = 129

[tex]n_2[/tex] = sample of households without pet dogs = 197

So, the test statistics = [tex]\frac{(0.08-0.12)-(0)}{\sqrt{\frac{0.08(1-0.08)}{129}+\frac{0.12(1-0.12)}{197} } }[/tex]

= -1.202

The value of z test statistics is -1.202.