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 α = 0.01 to test the claim that Find the critical value(s) for this hypothesis test. Does the data support the claim that a smaller proportion of households with pet dogs are burglarized? Number of households in sample with dogs is 208, without dogs is 126. Number of houses burglarized with dogs is 21, without dogs is 15.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

p1cap = X1/N1 = 126/208 = 0.6058
p1cap = X2/N2 = 15/21 = 0.7143
pcap = (X1 + X2)/(N1 + N2) = (126+15)/(208+21) = 0.6157

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.6058-0.7143)/sqrt(0.6157*(1-0.6157)*(1/208 + 1/21))
z = -0.97

P-value Approach
P-value = 0.1650
As P-value >= 0.01, fail to reject null hypothesis.