SOLUTION: Can someone please help me figure out how to work this out: It is claimed that the students at a certain university in Michigan will score an average of 85 on a given test. Is

Question 864667: Can someone please help me figure out how to work this out:
It is claimed that the students at a certain university in Michigan will score an average of 85 on a given test. Is the claim reasonable if a random sample of test scores from this university yields 83, 92, 88, 87, 80, and 92? Assume test results are normally distributed.
22Complete a hypothesis test at = 0.05 using the p-value approach.

Thanks!

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It is claimed that the students at a certain university in Michigan will score an average of 85 on a given test. Is the claim reasonable if a random sample of test scores from this university yields 83, 92, 88, 87, 80, and 92? Assume test results are normally distributed.
22Complete a hypothesis test at = 0.05 using the p-value approach.
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Ho: u = 85 (claim)
Ha: u # 85
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sample mean:: (83+92+88+87+80+92)/5 = 87
s = 4.82
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t(87) = (87-85)/[4.82/sqrt(6)] = 2/1.9678 = 1.01
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p-value = 2*P(t> 1.01 when df = 5) = 2*tcdf(1.01,100,5) = 0.36
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Since the p-value is greater than 5%, fail to reject Ho.
Conclusion: The claim is reasonable at the 5% confidence level.
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Cheers,
Stan H.
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