SOLUTION: 9.63 In the Big Ten (the NCAA sports league) a sample showed that only 267 out of 584 freshmen football players graduated within 6 years. (a) At α = .05 does this sample cont

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Question 141843: 9.63 In the Big Ten (the NCAA sports league) a sample showed that only 267 out of 584 freshmen football
players graduated within 6 years. (a) At α = .05 does this sample contradict the claim that at
least half graduate within 6 years? State your hypotheses and decision rule. (b) Calculate the
p-value and interpret it. (c) Do you think the difference is important, as opposed to significant?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In the Big Ten (the NCAA sports league) a sample showed that only 267 out of 584 freshmen football players graduated within 6 years.
(a) At α = .05 does this sample contradict the claim that at least half graduate within 6 years? State your hypotheses and decision rule.
Ho: p>=0.5 ; Ha:p< 0.5
p-hat = 267/584 = 0.457..
Critical value for one-tail test with alpha = 5%: z=1.645
Test statistic: z(0.457) = (0.457-0.5)/sqrt[0.5*0.5/584] = -2.0783...
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(b) Calculate the p-value and interpret it.
p-value = P(-10 < z< -2.0783) = 0.0188..
The probability the test results would give stronger evidence for rejecting
Ho is 1.88%
Since p-value is less than 5%, reject Ho.
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(c) Do you think the difference is important, as opposed to significant?
Since p-value is so small it is important; the Big Ten is lying.
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Cheers,
Stan H.