document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152873>Question 1152873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of 16 pharmacy customers showed the waiting times below (in minutes). Find a 90 percent confidence interval for μ, assuming that the sample is from a normal population.<BR>\n" );
document.write( "15 19 16 18 10 20 19 13<BR>\n" );
document.write( "22 9 19 22 18 20 24 19 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774987 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=774987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given Data Set = {15,19,16,18,10,20,19,13,22,9,19,22,18,20,24,19}<BR>\n" );
document.write( "n = 16<BR>\n" );
document.write( "because n > 30 is not true, and because we don't know sigma (population standard deviation), we use a T distribution<BR>\n" );
document.write( "df = n-1 = 16-1 = 15 degrees of freedom\r<BR>\n" );
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document.write( "Use a calculator or spreadsheet program to find these two values<BR>\n" );
document.write( "xbar = sample mean = 17.6875<BR>\n" );
document.write( "s = sample standard deviation = 4.1748253456 which is approximate\r<BR>\n" );
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document.write( "In the back of your stats textbook is a t table that looks similar to this shown here<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "Using that table specifically, highlight the entire row that starts with df = 15. Highlight the column that represents the 90% confidence level (see the bottom portion of the table).<BR>\n" );
document.write( "The value 1.753 is in this row and column. Therefore, t = 1.753 is the approximate critical value.<BR>\n" );
document.write( "Note: P(|T| < 1.753) = 0.90 which is another way of saying P(-1.753 < T < 1.753) = 0.90\r<BR>\n" );
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document.write( "Now onto computing the lower (L) and upper (U) bounds of the confidence interval.<BR>\n" );
document.write( "L = lower bound of confidence interval<BR>\n" );
document.write( "L = xbar - t*(s/sqrt(n))<BR>\n" );
document.write( "L = 17.6875 - 1.753*(4.1748253456/sqrt(16))<BR>\n" );
document.write( "L = 17.6875 - 1.753*(4.1748253456/4)<BR>\n" );
document.write( "L = 17.6875 - 1.753*(1.0437063364)<BR>\n" );
document.write( "L = 17.6875 - 1.8296172077092<BR>\n" );
document.write( "L = 15.8578827922908<BR>\n" );
document.write( "L = 15.86\r<BR>\n" );
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document.write( "U = upper bound of confidence interval<BR>\n" );
document.write( "U = xbar + t*(s/sqrt(n))<BR>\n" );
document.write( "U = 17.6875 + 1.753*(4.1748253456/sqrt(16))<BR>\n" );
document.write( "U = 17.6875 + 1.753*(4.1748253456/4)<BR>\n" );
document.write( "U = 17.6875 + 1.753*(1.0437063364)<BR>\n" );
document.write( "U = 17.6875 + 1.8296172077092<BR>\n" );
document.write( "U = 19.5171172077092<BR>\n" );
document.write( "U = 19.52\r<BR>\n" );
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document.write( "(L,U) = (15.86,19.52)\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "The 90% confidence interval is approximately (15.86,19.52)\r<BR>\n" );
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document.write( "We can write the confidence interval in the form L < mu < U which means we would have 15.86 < mu < 19.52\r<BR>\n" );
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document.write( "Yet another alternative is to write the confidence interval in the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \overline{x} \pm MoE\"> (MoE stands for Margin of Error), so we would get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 17.69 \pm 1.83\"> when rounding to 2 decimal places.<BR>\n" );
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