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 H |
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Accept H |
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Reject H |
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Reject H |

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

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