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 p_1<p_2p1​<p2​ 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?

	Household with Dog	Household without Dog
Number of households in sample	209	117
Number of households burglarized	20	12

z = -1.96; yes

z = 2.33; yes

z = -2.33; no

z = -2.575; no

Answer 1

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 = 20/209 = 0.0957
p1cap = X2/N2 = 12/117 = 0.1026
pcap = (X1 + X2)/(N1 + N2) = (20+12)/(209+117) = 0.0982

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.096-0.103)/sqrt(0.0982*(1-0.0982)*(1/209 + 1/117))
z = -0.2

z = -2.33; no