A simple random sample of front-seat occupants involved in car crashes is obtain
ID: 3224290 • Letter: A
Question
A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2871 occupants not wearing seat belts, 30 were killed. Among 7818 occupants wearing seat belts, 15 were killed. Use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities.
Test the claim using a hypothesis test.
Identify the test statistic.
Identify the P-value.
What is the conclusion based on the hypothesis test?
Test the claim by constructing an appropriate confidence interval.
What do the results suggest about the effectiveness of seat belts?
Explanation / Answer
Hypothesis:
Ho : p1 = p2
Ha: p1 < p2
Test statistic:
p1 = 30 / 2871 = 0.01 , n1 = 2871 , p2 = 15/7818=0.002 , n2 = 7818
p = (p1 * n1 + p2 * n2) / (n1 + n2)
= [(0.01 * 2871) + (0.002 * 7818)] / (2871+ 7818)
= 0.004
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt [ 0.004 * 0.996 * ( 1/2871 + 1/7818 ) ]
= 0.001
z = (p1 - p2) / SE
= (0.01 - 0.002)/0.001
= 8
P value is calculated using z = 8
P value = 0.00001.
As p value is less than 0.05 so we reject the null hypothesis
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