document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461981>Question 461981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The recent default rate on all student loans is 5.2 percent. In a recent random sample of 300 loans at private universities there were 9 defaults.<BR>\n" );
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document.write( "Does this sample show sufficient evidence that the private university loan default rate is below the rate for all universities, using a left-tailed test at &#945; = .01?\r<BR>\n" );
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document.write( "(a-1) 	Choose the appropriate hypothesis.\r<BR>\n" );
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document.write( "(a-2) 	\r<BR>\n" );
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document.write( "What is the z score for the sample data? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)\r<BR>\n" );
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document.write( "  z value 	 <BR>\n" );
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document.write( "(a-3) 	Should the null hypothesis be rejected?\r<BR>\n" );
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document.write( "(b) 	Calculate the p-value. (Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( "  p-value 	 <BR>\n" );
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document.write( "(c) 	The assumption of normality is justified.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316758 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=316758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The recent default rate on all student loans is 5.2 percent. In a recent random sample of 300 loans at private universities there were 9 defaults.\r<BR>\n" );
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document.write( "Does this sample show sufficient evidence that the private university loan default rate is below the rate for all universities, using a left-tailed test at &#945; = .01? <BR>\n" );
document.write( "(a-1) Choose the appropriate hypothesis.<BR>\n" );
document.write( "Ho: p >= 0.052<BR>\n" );
document.write( "Ha: p < 0.052<BR>\n" );
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document.write( "(a-2) <BR>\n" );
document.write( "What is the z score for the sample data? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) <BR>\n" );
document.write( "test statistic::: z(9/300) = ( 0.03-0.052)/sqrt[0.052*0.948/300] -1.7162<BR>\n" );
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document.write( "(a-3) Should the null hypothesis be rejected?<BR>\n" );
document.write( "p-value = P(z < -1.7162) = 0.0431<BR>\n" );
document.write( "Since the p-value is greater than 1%, <BR>\n" );
document.write( "fail to reject Ho at the 1% level.<BR>\n" );
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document.write( "(b) Calculate the p-value. (Round your answer to 4 decimal places.) <BR>\n" );
document.write( "p-value<BR>\n" );
document.write( "Done \r<BR>\n" );
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document.write( "(c) The assumption of normality is justified.<BR>\n" );
document.write( "I'll leave that to you.  Check your textbook.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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