Question 144048:
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.
Ho: u<=250
Ha: u>250
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x-bar = 275.66 ; s = 78.11
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Critical value for one-tail test when alpha =5% and df=24: t=1.711
test statistic:
t(275.66)= (275.66-250)/[78.11/sqrt(25)] = 1.6426
p-value: P(1.6426 < t < 10; df=24) = 0.0568
Conclusion:
Since p-value is greater than 5%, fail to reject Ho.
The mean out-of-pocket payment is not statistically greater than $250
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(b) Is this a close decision?
Yes because the p-value is quite close to 5%
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Cheers,
Stan H.
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