Question 185306: An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than $250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $78.11.
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(a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than $250 out-of-pocket? State your hypotheses and decision rule.
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Ho: u <= 250
Ha: u > 250
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Critical value for a right-tailed test with alpha = 5%, df=24: t=1.711
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Test Statistic:
t(275.66) = (275.66-250)/[78.11/sqrt(25)] = 1.643
p-value = P(t > 1.643) = 0.05676
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Conclusion: Since the p-value is greater than 5%, Fail to reject Ho.
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(b) Is this a close decision?
Yes, very close as the p-value is "close" to 5%.
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Cheers,
Stan H.
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