document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=247011>Question 247011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, is the average spending in the northern region significantly less than the average spending in the southern region at the 1 percent level? (a) State the hypotheses and decision rule. (b) Find the test statistic assuming unequal variances. (c) State your conclusion. Is this a strong conclusion? (d) Can you suggest reasons why a difference might exist?\r<BR>\n" );
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document.write( "Medicare Spending per Patient (adjusted for age, sex, and race)<BR>\n" );
document.write( "Statistic                      Northern Region   Southern Region<BR>\n" );
document.write( "Sample mean                    $3,123            $8,456<BR>\n" );
document.write( "Sample standard deviation      $1,546            $3,678<BR>\n" );
document.write( "Sample size                     14 patients       16 patients </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180287 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=180287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Medicare spending per patient in different U.S. metropolitan areas may differ. Based on the sample data below, is the average spending in the northern region significantly less than the average spending in the southern region at the 1 percent level? <BR>\n" );
document.write( "(a) State the hypotheses and decision rule.<BR>\n" );
document.write( "Ho: u(south)-u(north) > 0<BR>\n" );
document.write( "H1: u(south)-u(north) <= 0<BR>\n" );
document.write( "Rule: Reject Ho if p-value < 1%<BR>\n" );
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document.write( "(b) Find the test statistic assuming unequal variances.<BR>\n" );
document.write( "I ran a 2 Sample t-test and got the following:<BR>\n" );
document.write( "ts = 5.2903<BR>\n" );
document.write( "p = 100%<BR>\n" );
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document.write( "(c) State your conclusion. Is this a strong conclusion?<BR>\n" );
document.write( "Since the p-value is greater than 1%, fail to reject Ho.<BR>\n" );
document.write( "North average is is much less than south average.<BR>\n" );
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document.write( "(d) Can you suggest reasons why a difference might exist?<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
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document.write( "Medicare Spending per Patient (adjusted for age, sex, and race)<BR>\n" );
document.write( "Statistic;;;;;;;;;;; Northern Region;;;;;;;;;; Southern Region<BR>\n" );
document.write( "Sample mean;;;;;;;;;;;;;; $3,123;;;;;;;;;;;;;;;;;; $8,456<BR>\n" );
document.write( "Sample standard deviation $1,546;;;;;;;;;;;;;;;;;; $3,678<BR>\n" );
document.write( "Sample size;;;;;;;;;;;;; 14 patients;;;;;;;;;;;;; 16 patients<BR>\n" );
document.write( "==================================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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