document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980616>Question 980616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the given degree of confidence and sample data to construct a confidence interval for the population mean &#956;. Assume<BR>\n" );
document.write( "that the population has a normal distribution.<BR>\n" );
document.write( " n = 10, x = 8.1, s = 4.8, 95% confidence </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601746 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=601746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> xbar = 8.1<BR>\n" );
document.write( "n = 10<BR>\n" );
document.write( "s = 4.8<BR>\n" );
document.write( "Since n = 10 makes n > 30 false, and because sigma is not known, we use a T distribution. The critical t value is t = 2.262 (at 95% confidence, df = n-1 = 10-1 = 9). Use a <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">table</a> to find this\r<BR>\n" );
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document.write( "The confidence interval is of the form (L,U) where L is the lower limit and U is the upper limit.\r<BR>\n" );
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document.write( "Lower Limit (L):<BR>\n" );
document.write( "L = xbar - t*s/sqrt(n)<BR>\n" );
document.write( "L = 8.1 - 2.262*4.8/sqrt(10)<BR>\n" );
document.write( "L = 8.1 - 2.262*1.51789327688082<BR>\n" );
document.write( "L = 8.1 - 3.43347459230442<BR>\n" );
document.write( "L = 4.66652540769558<BR>\n" );
document.write( "L = 4.67\r<BR>\n" );
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document.write( "Upper Limit (U):<BR>\n" );
document.write( "U = xbar + t*s/sqrt(n)<BR>\n" );
document.write( "U = 8.1 + 2.262*4.8/sqrt(10)<BR>\n" );
document.write( "U = 8.1 + 2.262*1.51789327688082<BR>\n" );
document.write( "U = 8.1 + 3.43347459230442<BR>\n" );
document.write( "U = 11.5334745923044<BR>\n" );
document.write( "U = 11.53\r<BR>\n" );
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document.write( "The 95% confidence interval for mu is (L,U) = (4.67, 11.53)\r<BR>\n" );
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document.write( "Note: The confidence interval can also be stated as 4.67 < mu < 11.53. Some books will use plus/minus notation and say <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 8.1 \pm 3.43347\"> where 8.1 is the point estimate (xbar) and 3.43347 is the margin of error. </SPAN>\n" );
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