document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174373>Question 174373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129344 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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. <BR>\n" );
document.write( "(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. <BR>\n" );
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document.write( "Ho: u = 250<BR>\n" );
document.write( "Ha: u > 250<BR>\n" );
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document.write( "Critical value for a one-tail test with alpha = 5%: z = 1.645<BR>\n" );
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document.write( "Test statistic: z(275.66) = (275.66-250)/[78.11/Sqrt(25)] = 1.6456<BR>\n" );
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document.write( "Conclusion: Since the TS is not in the reject interval, Fail to reject Ho.<BR>\n" );
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document.write( "(b) Is this a close decision?<BR>\n" );
document.write( "Yes, the test statistic is very close to the critical value.<BR>\n" );
document.write( "p-value = P(z > 1.6456) = 0.05024, which is very close to the alpha value.<BR>\n" );
document.write( "There are only 5.024% of test results that could have provided stronger<BR>\n" );
document.write( "evidence for rejecting Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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