document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204924>Question 1204924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We are interested in finding out what proportion of borrowers default on a credit card loan. We sample 100 credit cards. We find that 10 default.<BR>\n" );
document.write( "(A) Find proportion of credit card borrowers that default <BR>\n" );
document.write( "(B) Construct a 80% Confidence Interval <BR>\n" );
document.write( "(C) Construct a 99% Confidence Interval <BR>\n" );
document.write( "(D) What does your findings interpret? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841668 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 100.<BR>\n" );
document.write( "10 out of the 100 default.<BR>\n" );
document.write( "that's a mean proportion of .1<BR>\n" );
document.write( "standard error is equal to sqrt(.1 * .9 / 100) = .03<BR>\n" );
document.write( "critical z-score for 80% confidence interval is z = plus or minus 1.28155.<BR>\n" );
document.write( "critical z-score for 90% confidence interval is z = plus or minus 1.64485.<BR>\n" );
document.write( "z-score formula is z = (x-m)/s<BR>\n" );
document.write( "z is the z-score.<BR>\n" );
document.write( "x is the critical proportion.<BR>\n" );
document.write( "m is the mean proportion.<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "you have z.<BR>\n" );
document.write( "you need to solve for x.\r<BR>\n" );
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document.write( "at 80% confidence interval:<BR>\n" );
document.write( "the high side of the confidence interval formula is 1.28155 = (x - .1) / .03.<BR>\n" );
document.write( "solve for x to get x = 1.28155 * .03 + .1 = .1384465.<BR>\n" );
document.write( "the low side of the confidence interval formula is -1.28155 = (x - .1) / .03.<BR>\n" );
document.write( "solve for x to get x = -1.28155 * .03 + .1 = .0615535.<BR>\n" );
document.write( "your 80% confidence interval is from .0615535 to .1384465.\r<BR>\n" );
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document.write( "at 90% confidence interval:<BR>\n" );
document.write( "the high side of the confidence interval formula is 1.64485 = (x - .1) / .03.<BR>\n" );
document.write( "solve for x to get x = 1.64485 * .03 + .1 = .1493455.<BR>\n" );
document.write( "the low side of the confidence interval formula is -1.64485 = (x - .1) / .03.<BR>\n" );
document.write( "solve for x to get x = -1.64485 * .03 + .1 = .0506545.<BR>\n" );
document.write( "your 90% confidence interval is from .0506545 to .1493455.\r<BR>\n" );
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document.write( "here's what 80% and 90% confidence intervals look like on a graph.<BR>\n" );
document.write( "the mean proportion is .1 (10/100 = .1)<BR>\n" );
document.write( "the standard error is .03 (sqrt(.1*.9/100))\r<BR>\n" );
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