Question 130409
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. 
Ho: mu= 250
Ha: mu > 250
Critical value for alpha = 5% and df = 24  is t = 1.711
Test statistic: 
t(275.66) = (275.66-250)/[78.11/sqrt(25)] = 25.66*5/78.11 = 1.643
Since the test statistic is less than the critical value Fail to 
reject Ho.
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(b) Is this a close decision?
The p-value for t= 1.643 is 0.05675...
Very close to 5% which is the breakpoint for deciding rejection of Ho.
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Cheers,
Stan H.