Question 324841: For a simple random sample of 100 cars of a certain popular model in 2003, it was found that 20 had a certain minor defect in the brakes. For an independent SRS of 400 cars of the same model in 2004, it was found that 50 had the same defect. Let p1 and p2 be the proportions of all cars of this model in 2003 and 2004, respectively, that have the defect. We wish to test H0: p1 = p2 against Ha: p1 > p2. For this test, the (approximate) P-value is
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For a simple random sample of 100 cars of a certain popular model in 2003, it was found that 20 had a certain minor defect in the brakes.
phat1 = 20/100 = 0.2
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For an independent SRS of 400 cars of the same model in 2004, it was found that 50 had the same defect.
phat2 = 50/400 = 0.125
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test stat: z = (0.2-0.125)/sqrt[(0.2*0.8/100) + (0.125*0.875/400)] = 1.7328
Let p1 and p2 be the proportions of all cars of this model in 2003 and 2004, respectively, that have the defect. We wish to test H0: p1 = p2 against Ha: p1 > p2. For this test, the (approximate) P-value is
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p-value = 2*P(z> 1.7328) = 0.0831
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Cheers,
Stan H.
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