Question 269561: I am so confused by this question. Can someone please help me with this? Thank you.
A medical school claims that more than 28% of its students plan to go into general practice.
a. It is found that among a random sample of 130 of the school’s students, 42 of them plan to go into general practice. Does this sample evidence support the school’s claim? Use the p-value approach and alpha = 0.05 to make your decision.
b. Suppose a second sample is collected a year after the first with the results indicating 57 out of 135 plan to go into general practice. Does this sample evidence support the school’s claim? Use the p-value approach and alpha = 0.05 to make your decision.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A medical school claims that more than 28% of its students plan to go into general practice.
a. It is found that among a random sample of 130 of the school’s students, 42 of them plan to go into general practice. Does this sample evidence support the school’s claim? Use the p-value approach and alpha = 0.05 to make your decision.
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Ho: p <= 0.28
H1: p > 0.28 (school claim)
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sample proportion = phat = 42/130 = 0.323
test stat: z(0.323) = (0.323-0.28)/sqrt(0.28*0.72/130) = 1.0939
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p-value for right-tail test with alpha - 5% = P(z> 1.0939)
= normalcdf(1.0929,100) = 0.1370
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Conclusion: Since the p-value is greater than 5%, fail to reject Ho.
The test does not support the school claim at the 5% significance level.
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b. Suppose a second sample is collected a year after the first with the results indicating 57 out of 135 plan to go into general practice. Does this sample evidence support the school’s claim? Use the p-value approach and alpha = 0.05 to make your decision.
phat = 57/135 = 0.42
z(0.42) = (0.42-0.28)/sqrt(0.28*0.72/135) = 3.6228
P-value = P(z> 3.6228) = normalcdf(3.6228,100) = 0.0001457
Conclusion: Since the p-value is less than 5%, reject Ho.
The test supports the school claim at the 5% significance level.
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Cheers,
Stan H.
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