document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183062>Question 1183062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average student-loan debt is reported to be $25,235.<BR>\n" );
document.write( "A student believes that the student-loan debt us higher in her area.<BR>\n" );
document.write( "She takes a random sample of 100 college students in her area and determines the mean student-loan debt is $27,524 and the standard deviation is $6,000.<BR>\n" );
document.write( "Is there sufficient evidence to support the student's claim at a 5% significance level?\r<BR>\n" );
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document.write( "a) Is it safe to assume that n < 5% of all college students in the local area?<BR>\n" );
document.write( "   = Yes\r<BR>\n" );
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document.write( "b) Is n = 30? Yes\r<BR>\n" );
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document.write( "Test the claim:\r<BR>\n" );
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document.write( "a) Determine the null and alternative hypothesis.<BR>\n" );
document.write( "Enter the correct symbol and value.\r<BR>\n" );
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document.write( "Ho: u = _________\r<BR>\n" );
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document.write( "Ha: u = > _________\r<BR>\n" );
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document.write( "b) Determine the test statistic.\r<BR>\n" );
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document.write( "Round to 2 decimals<BR>\n" );
document.write( "    t = ______\r<BR>\n" );
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document.write( "c) Find the p-value\r<BR>\n" );
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document.write( "Round to 4 decimals\r<BR>\n" );
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document.write( "    p = ______\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813230 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=813230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is safe to assume n is < 5% of all students if one thinks there are more than 2000 students in the area, since the sample is 100/2000 in that instance or 5%.<BR>\n" );
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document.write( "Ho:mu < = $25,235<BR>\n" );
document.write( "Ha: mu >$25,235<BR>\n" );
document.write( "Note: I prefer the  greater than (without equals) in Ha and put the inequality and equal sign with Ho, since rejecting it means that single value postulated is rejected as well.<BR>\n" );
document.write( "alpha=0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "test stat is t(0.975, df=99) can use z, but it is a t-test and no reason not to use it in these days of calculators.<BR>\n" );
document.write( "Critical value for a right tail test is t > 1.66<BR>\n" );
document.write( "t=(x bar-mu)/s/sqrt(n)<BR>\n" );
document.write( "=$2289*10/6000, inverting the denominator to multiply.<BR>\n" );
document.write( "=3.815 or 3.82\r<BR>\n" );
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document.write( "This is > 1.66 so reject Ho and conclude that student debt is higher than the postulated value.<BR>\n" );
document.write( "p-value=0.0001 </SPAN>\n" );
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