document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193737>Question 1193737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a study of speed​ dating, male subjects were asked to rate the attractiveness of their female​ dates, and a sample of the results is listed below ​(1=not ​attractive; 10=extremely ​attractive). Construct a confidence interval using a 99​% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult​ females?\r<BR>\n" );
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document.write( "8, 7, 2, 8, 6, 6, 7, 8, 7, 9, 3, 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825775 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=825775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are n = 12 items in this sample.\r<BR>\n" );
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document.write( "Use your calculator to compute the mean and sample standard deviation of the given data values<BR>\n" );
document.write( "xbar = 6.58333 = sample mean<BR>\n" );
document.write( "s = 2.10878 = sample standard deviation<BR>\n" );
document.write( "both of which are approximate\r<BR>\n" );
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document.write( "Use a table like this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "to look at the bottom row marked in blue (it starts with Z)<BR>\n" );
document.write( "The value 2.576 is just above the 99% confidence level.\r<BR>\n" );
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document.write( "The z critical value is roughly z = 2.576 when we have 99% confidence level.\r<BR>\n" );
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document.write( "E = margin of error<BR>\n" );
document.write( "E = z*s/sqrt(n)<BR>\n" );
document.write( "E = 2.576*2.10878/sqrt(12)<BR>\n" );
document.write( "E = 1.56815<BR>\n" );
document.write( "which is approximate.\r<BR>\n" );
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document.write( "L = lower bound of the confidence interval<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 6.58333 - 1.56815<BR>\n" );
document.write( "L = 5.01518<BR>\n" );
document.write( "L = 5.02\r<BR>\n" );
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document.write( "U = upper bound of the confidence interval<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 6.58333 + 1.56815<BR>\n" );
document.write( "U = 8.15148<BR>\n" );
document.write( "U = 8.15\r<BR>\n" );
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document.write( "The 99% confidence interval is approximately <font color=red>(5.02, 8.15)</font> when presented in the template of (L, U)\r<BR>\n" );
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document.write( "This is equivalent to 5.02 < mu < 8.15 when written in the form L < mu < U<BR>\n" );
document.write( "We're 99% confident the true population mean attractiveness rating is somewhere between a rating of 5.02 and 8.15<BR>\n" );
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