Question

The proportion of cars stolen that do not have a burglar alarm installed is 10% in a sample of 40 cars. The proportion of cars stolen that do have a burglar alarm installed is 5%, also in a sample of 40 cars. What would be the conclusion at α = 0.05 if you want to claim that the proportion of cars that do not have a burglar alarm installed is more than the proportion of cars with burglar alarms installed?

		Accept H0, because the test statistic is less than 1.65.
		Accept H0, because the test statistic is less than 1.96.
		Reject H0, because the test statistic is more than 1.65.
		Reject H0, because the test statistic is more than 1.96

Answer 1

p1cap = X1/N1 = 4/40 = 0.1
p1cap = X2/N2 = 2/40 = 0.05
pcap = (X1 + X2)/(N1 + N2) = (4+2)/(40+40) = 0.075

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

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1-0.05)/sqrt(0.075*(1-0.075)*(1/40 + 1/40))
z = 0.85

Option A