document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176712>Question 1176712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia on a recent day. It is reasonable to assume that the population is approximately normal.\r<BR>\n" );
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document.write( "4.750\r<BR>\n" );
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document.write( "4.375\r<BR>\n" );
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document.write( "4.176\r<BR>\n" );
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document.write( "4.679\r<BR>\n" );
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document.write( "4.426\r<BR>\n" );
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document.write( "4.227\r<BR>\n" );
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document.write( "4.125\r<BR>\n" );
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document.write( "4.250\r<BR>\n" );
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document.write( "3.950\r<BR>\n" );
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document.write( "4.191\r<BR>\n" );
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document.write( "4.299\r<BR>\n" );
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document.write( "4.415\r<BR>\n" );
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document.write( "Source: www.bankrate.com<BR>\n" );
document.write( "a.\r<BR>\n" );
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document.write( "Construct a 99% confidence interval for the mean rate.\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "One week earlier, the mean rate was 4.050%. A mortgage broker claims that the mean rate is now higher. Based on the confidence interval, is this a reasonable claim? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803995 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 4.322 %<BR>\n" );
document.write( "sd is 0.226%<BR>\n" );
document.write( "99% half CI is t (0.995, df=11)*s/sqrt(n)<BR>\n" );
document.write( "=3.106*0.226/sqrt(12)<BR>\n" );
document.write( "=0.203<BR>\n" );
document.write( "the 99% interval is (4.119, 4.525) units %<BR>\n" );
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document.write( "Because 4.050% is outside the interval, it is reasonable to claim the true rate has risen. We are 99% confident that the true value, whatever it is, lies within the interval. </SPAN>\n" );
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