document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265560>Question 265560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me understand this question?\r<BR>\n" );
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document.write( "A 99% confidence interval (in inches) for the mean height of a population is 65.44 < &#956; < 66.96.  This result is based on a sample size of 144.  If the confidence interval 65.65 < &#956; < 66.75 is obtained from the same sample data, what is the degree of confidence?  \r<BR>\n" );
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document.write( "a.  You will first need to find the sample mean and sample standard deviation based on the confidence interval given.<BR>\n" );
document.write( "b.  Use the value you found in part a to determine the degree of confidence for the interval 65.65 < &#956; < 66.75 is based on.<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 #195367 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=195367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A 99% confidence interval (in inches) for the mean height of a population is 65.44 < &#956; < 66.96.<BR>\n" );
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document.write( "This result is based on a sample size of 144.<BR>\n" );
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document.write( "If the confidence interval 65.65 < &#956; < 66.75 is obtained from the same sample data, what is the degree of confidence?<BR>\n" );
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document.write( "a. You will first need to find the sample mean and sample standard deviation based on the confidence interval given.<BR>\n" );
document.write( "The width of the confidence interval is 2E<BR>\n" );
document.write( "2E = 66.96-65.44 = 1.52<BR>\n" );
document.write( "E = 0.76<BR>\n" );
document.write( "But E = z*s/sqrt(144) and z = invNorm(0.995) = 2.5758..<BR>\n" );
document.write( "So 0.76 = 2.5758<BR>\n" );
document.write( "And s = 3.54 (sample standard deviation)<BR>\n" );
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document.write( "Since xbar-E = 65.44<BR>\n" );
document.write( "xbar - 0.76 = 65.44<BR>\n" );
document.write( "xbar = 66.2 (sample mean)<BR>\n" );
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document.write( "b. Use the value you found in part a to determine the degree of confidence for the interval 65.65 < &#956; < 66.75 is based on.<BR>\n" );
document.write( "66.2-E = 65.65<BR>\n" );
document.write( "E = 0.55<BR>\n" );
document.write( "But E = z*s/sqrt(144)<BR>\n" );
document.write( "0.55 = z*3.54/sqrt(144)<BR>\n" );
document.write( "z = 1.8644<BR>\n" );
document.write( "normalcdf(-100,-1.8644) = 0.03<BR>\n" );
document.write( "Therefore the degree of confidence is 94%<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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