document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207748>Question 1207748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct the indicated confidence interval for the population mean mu using the​ t-distribution. Assume the population is normally distributed.<BR>\n" );
document.write( "cequals0.98​,  x overbarequals13.6​,  sequals0.94​,  nequals19 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845793 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=845793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "xbar = sample mean<BR>\n" );
document.write( "s = sample standard deviation<BR>\n" );
document.write( "n = sample size<BR>\n" );
document.write( "df = degrees of freedom\r<BR>\n" );
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document.write( "xbar = 13.6<BR>\n" );
document.write( "s = 0.94<BR>\n" );
document.write( "n = 19<BR>\n" );
document.write( "df = n-1 = 19-1 = 18 \r<BR>\n" );
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document.write( "Use a T table such as 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( "Similar tables should be found in the back of your stats textbook.<BR>\n" );
document.write( "Use that table to determine the t critical value is roughly t =  2.552 at a 98% confidence level and when df = 18.<BR>\n" );
document.write( "The confidence levels are labeled at the bottom.<BR>\n" );
document.write( "What this indicates is that P(-2.552 < T < 2.552) = 0.98 approximately when df = 18.\r<BR>\n" );
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document.write( "Let's compute the margin of error.<BR>\n" );
document.write( "E = t*s/sqrt(n)<BR>\n" );
document.write( "E = 2.552*0.94/sqrt(19)<BR>\n" );
document.write( "E = 0.55034082 approximately\r<BR>\n" );
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document.write( "Use this to find the lower and upper bounds (L and U)<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 13.6 - 0.55034082<BR>\n" );
document.write( "L = 13.04965918<BR>\n" );
document.write( "L = 13.05\r<BR>\n" );
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document.write( "U = xbar + E<BR>\n" );
document.write( "U = 13.6 + 0.55034082<BR>\n" );
document.write( "U = 14.15034082<BR>\n" );
document.write( "U = 14.15\r<BR>\n" );
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document.write( "Depending how you round the final answer, the 98% confidence interval for the population mean is approximately <font color=red>(13.05, 14.15)</font><BR>\n" );
document.write( "This is in the format (L, U)\r<BR>\n" );
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document.write( "Another way to express the confidence interval would be to say <font color=red>13.05 < mu < 14.15</font><BR>\n" );
document.write( "This is of the format L < mu < U which I think is more descriptive since we're involving the parameter being estimated (mu).<BR>\n" );
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