document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130409>Question 130409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining<BR>\n" );
document.write( "that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a<BR>\n" );
document.write( "standard deviation of $78.11. (a) At the 5 percent level of significance, does this sample prove a<BR>\n" );
document.write( "violation of the guideline that the average patient should pay no more than $250 out-of-pocket?<BR>\n" );
document.write( "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 #95288 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=95288\">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?<BR>\n" );
document.write( "State your hypotheses and decision rule. <BR>\n" );
document.write( "Ho: mu= 250<BR>\n" );
document.write( "Ha: mu > 250<BR>\n" );
document.write( "Critical value for alpha = 5% and df = 24  is t = 1.711<BR>\n" );
document.write( "Test statistic: <BR>\n" );
document.write( "t(275.66) = (275.66-250)/[78.11/sqrt(25)] = 25.66*5/78.11 = 1.643<BR>\n" );
document.write( "Since the test statistic is less than the critical value Fail to <BR>\n" );
document.write( "reject Ho.<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(b) Is this a close decision?<BR>\n" );
document.write( "The p-value for t= 1.643 is 0.05675...<BR>\n" );
document.write( "Very close to 5% which is the breakpoint for deciding rejection of Ho.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );