document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143854>Question 1143854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A data set includes 107 body temperatures of healthy adult humans having a mean of 98.7degreesF and a standard deviation of 0.72degreesF. Construct a 99​% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6degreesF as the mean body​ temperature?\r<BR>\n" );
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document.write( "What is the confidence interval estimate of the population mean mu​?\r<BR>\n" );
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document.write( "What does this suggest about the use of 98.6degreesF as the mean body​ temperature?<BR>\n" );
document.write( "A.<BR>\n" );
document.write( "This suggests that the mean body temperature could be higher than 98.6degreesF.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "This suggests that the mean body temperature could be lower than 98.6degreesF.<BR>\n" );
document.write( "C.<BR>\n" );
document.write( "This suggests that the mean body temperature could very possibly be 98.6degreesF. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764807 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=764807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sample size of 107 is > 30, so we can use the Normal Distribution probability derived from the z-score tables.<BR>\n" );
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document.write( "The sample mean is 98.7 degrees F and the sample standard deviation is 0.72 degrees F<BR>\n" );
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document.write( "alpha(a) = 1 - 0.99 = 0.01<BR>\n" );
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document.write( "critical probability(p*) = 1 - a/2 = 0.995<BR>\n" );
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document.write( "the critical value(cv) is the z-score associated with p*, cv = 2.57<BR>\n" );
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document.write( "margin of error(me) = cv * standard deviation = 2.57 * 0.72 = 1.85<BR>\n" );
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document.write( "99% confidence interval is 98.7 + or - 1.85, (96.85, 100.55)<BR>\n" );
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document.write( "Using the same sampling method, we select different samples of size 107 and compute a different interval estimate for each sample. Some interval estimates would include the true population mean and some would not. A 99% confidence level means that we would expect 99% of the interval estimates to include the population mean.<BR>\n" );
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document.write( "answer is C.<BR>\n" );
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