document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174983>Question 1174983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. The mean serum cholesterol level in a certain population of normal healthy men<BR>\n" );
document.write( "is 240 mg/dl and the standard deviation is 40 mg/dl. A clinical researcher<BR>\n" );
document.write( "interested in comparing cholesterol levels in this healthy population with those<BR>\n" );
document.write( "in men with coronary artery disease measured serum cholesterol level in a<BR>\n" );
document.write( "random sample of 100men who had undergone coronary bypass surgery during<BR>\n" );
document.write( "the preceding two year period. The mean serum cholesterol level for sampling<BR>\n" );
document.write( "was 260 mg/dl<BR>\n" );
document.write( "A. What is the 95% confidence interval estimate of the mean cholesterol level for<BR>\n" );
document.write( "all men undergoing bypass surgery? Assume that the standard deviation of<BR>\n" );
document.write( "serum cholesterol measurement for this population is the same as that of the<BR>\n" );
document.write( "healthy population ( i.e., 40mg/dl)<BR>\n" );
document.write( "B. Based on this estimate, can the researcher conclude that the mean serum<BR>\n" );
document.write( "cholesterol of men undergoing coronary bypass surgery differs from that of<BR>\n" );
document.write( "healthy men?<BR>\n" );
document.write( "2. Among 200 patients at a Tikur Anbessa hospital.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800494 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=800494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll do the first problem to get you started.<BR>\n" );
document.write( "You should only post one question at a time please.\r<BR>\n" );
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document.write( "Part A\r<BR>\n" );
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document.write( "For the population of men undergoing the surgery, we have<BR>\n" );
document.write( "xbar = 260 mg/dl = sample mean, used to estimate population mean (mu)<BR>\n" );
document.write( "sigma = 40 mg/dl = population standard deviation<BR>\n" );
document.write( "n = 100 = sample size\r<BR>\n" );
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document.write( "At 95% confidence, the z critical value is roughly z = 1.960<BR>\n" );
document.write( "We're using the standard normal z distribution because we know the population standard deviation sigma.\r<BR>\n" );
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document.write( "The lower bound L of the confidence interval is:<BR>\n" );
document.write( "L = xbar - z*sigma/sqrt(n)<BR>\n" );
document.write( "L = 260 - 1.960*40/sqrt(100)<BR>\n" );
document.write( "L = 260 - 7.84<BR>\n" );
document.write( "L = 252.16\r<BR>\n" );
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document.write( "The upper bound U is<BR>\n" );
document.write( "U = xbar + z*sigma/sqrt(n)<BR>\n" );
document.write( "U = 260 + 1.960*40/sqrt(100)<BR>\n" );
document.write( "U = 260 + 7.84<BR>\n" );
document.write( "U = 267.84\r<BR>\n" );
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document.write( "The 95% confidence interval to estimate the mean population (mu) of the cholesterol level of the men undergoing surgery is (252.16, 267.84)<BR>\n" );
document.write( "We are 95% confident that mu is somewhere in the interval (252.16, 267.84)\r<BR>\n" );
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document.write( "We can express that interval as 252.16 < mu < 267.84\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "Yes we can conclude that the mean serum cholesterol for the men undergoing bypass surgery differs from the healthy men. <BR>\n" );
document.write( "This is because the interval 252.16 < mu < 267.84 does <u>not</u> contain mu = 240. This value is to the left of the lower bound 252.16\r<BR>\n" );
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document.write( "Since mu = 240 is not in the interval 252.16 < mu < 267.84, this means there's no way mu can be equal to 240 for the population of men undergoing surgery. \r<BR>\n" );
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document.write( "In other words, if A and B represent the population means for the healthy men vs the men undergoing surgery, then we can say:<BR>\n" );
document.write( "A = 240<BR>\n" );
document.write( "B = some value between 252.16 and 267.84<BR>\n" );
document.write( "clearly we can see that B = 240 is not possible and B > A and B > 252.16\r<BR>\n" );
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