document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202095>Question 1202095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If n=17,¯x(x-bar)=34, and s=4, construct a confidence interval at a 99% confidence level.<BR>\n" );
document.write( " Assume the data came from a normally distributed population.<BR>\n" );
document.write( "Give your answers to one decimal place.<BR>\n" );
document.write( "_____<μ<_____ </SPAN>\n" );
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document.write( "Answer:  <font color=red size=4>31.2 < mu < 36.8</font>\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "mu = μ = Greek letter representing population mean<BR>\n" );
document.write( "n = 17 = sample size<BR>\n" );
document.write( "xbar = 34 = sample mean<BR>\n" );
document.write( "s = 4 = sample standard deviation<BR>\n" );
document.write( "df = degrees of freedom = n-1 = 17-1 = 16\r<BR>\n" );
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document.write( "Because the population standard deviation (sigma) is not known, and because n > 30 isn't the case, we must use the T distribution.\r<BR>\n" );
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document.write( "Refer to this T table<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( "Locate the row labeled df = 16<BR>\n" );
document.write( "Locate the columnn labeled \"99% confidence\". The confidence labels are at the bottom. <BR>\n" );
document.write( "The approximate value t = 2.921 is at this row and column intersection. It is the t critical value.<BR>\n" );
document.write( "Specialized stats calculators such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.omnicalculator.com/statistics/critical-value\">https://www.omnicalculator.com/statistics/critical-value</a><BR>\n" );
document.write( "can find the t critical value. <BR>\n" );
document.write( "Make sure to do a two-tailed test. <BR>\n" );
document.write( "Also set the significance level to 0.01 (recall that alpha = 1-C where C is the confidence level)\r<BR>\n" );
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document.write( "Compute the margin of error<BR>\n" );
document.write( "E = t*s/sqrt(n)<BR>\n" );
document.write( "E = 2.921*4/sqrt(17)<BR>\n" );
document.write( "E = 2.833786<BR>\n" );
document.write( "That result is approximate.\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "L = lower boundary<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 34 - 2.833786<BR>\n" );
document.write( "L = 31.166214<BR>\n" );
document.write( "L = 31.2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "U = upper boundary<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 34 + 2.833786<BR>\n" );
document.write( "U = 36.833786<BR>\n" );
document.write( "U = 36.8\r<BR>\n" );
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document.write( "The 99% confidence interval in the format L < mu < U is roughly <font color=red size=4>31.2 < mu < 36.8</font>\r<BR>\n" );
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document.write( "That can be condensed to the format (L, U) so we get (31.2, 36.8)\r<BR>\n" );
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document.write( "We are 99% confident that the population mean (mu) is somewhere between 31.2 and 36.8<BR>\n" );
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