Question 127478This question is from textbook Applied Statistics in Business and Eco
: 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?
This question is from textbook Applied Statistics in Business and Eco
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. (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?
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Ho: mu <= 250
Ha: mu > 250
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Critical Value for one-tail t-test with alpha = 5% and 24 degrees of freedom
t = 1.711
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Test Statistic:
t(275.66-250)/[78.11/sqrt(25)] = 1.6426
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Conclusion: Fail to reject Ho because the test statistic is less than the
critical value. This sample does not prove a violation of the guideline.
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Is it a close decision?: The probability difference between t=1.6426 and
t=1.711 is about 0.0068 which is very small. A slight variation in
the test results could have caused us to reject Ho.
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Cheers,
Stan H.
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