document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202152>Question 1202152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The body temperatures in degrees Fahrenheit of a sample of adults in one small town are: 97.1	98.1	98	97.7	97.4	99.3	96.8\r<BR>\n" );
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document.write( "Assume body temperatures of adults are normally distributed. Based on this data, find the 90% confidence interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.\r<BR>\n" );
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document.write( "90% C.I. = <BR>\n" );
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document.write( "Answer:  <font color=red size=4>(97.169, 98.374)</font><BR>\n" );
document.write( "That is the condensed form of 97.169 < mu < 98.374\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\r<BR>\n" );
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document.write( "In this problem's context, mu is the population mean body temperature in degrees Fahrenheit.<BR>\n" );
document.write( "The goal is to estimate mu using a confidence interval.\r<BR>\n" );
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document.write( "Given data set = {97.1,98.1,98,97.7,97.4,99.3,96.8}<BR>\n" );
document.write( "n = 7 = sample size<BR>\n" );
document.write( "xbar = sample mean<BR>\n" );
document.write( "xbar = (add up the values)/(number of values)<BR>\n" );
document.write( "xbar = (97.1+98.1+98+97.7+97.4+99.3+96.8)/(7)<BR>\n" );
document.write( "xbar = 97.77143 approximately\r<BR>\n" );
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document.write( "Use a calculator or spreadsheet to determine the sample standard deviation is approximately s = 0.81999 \r<BR>\n" );
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document.write( "df = degrees of freedom = n-1 = 7-1 = 6\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 = 6<BR>\n" );
document.write( "Locate the column labeled \"90% confidence\". The confidence labels are at the bottom. <BR>\n" );
document.write( "The approximate value t = 1.943 is at this row and column intersection. It is the t critical value.\r<BR>\n" );
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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 0.10 (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 = 1.943*0.81999/sqrt(7)<BR>\n" );
document.write( "E = 0.60219<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 = 97.77143 - 0.60219<BR>\n" );
document.write( "L = 97.16924<BR>\n" );
document.write( "L = 97.169<BR>\n" );
document.write( "and<BR>\n" );
document.write( "U = upper boundary<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 97.77143 + 0.60219<BR>\n" );
document.write( "U = 98.37362<BR>\n" );
document.write( "U = 98.374\r<BR>\n" );
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document.write( "The 90% confidence interval in the format L < mu < U is roughly 97.169 < mu < 98.374\r<BR>\n" );
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document.write( "That is then condensed to the format (L, U) so we get <font color=red size=4>(97.169, 98.374)</font> as the final answer.\r<BR>\n" );
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document.write( "We are 90% confident that the population mean temperature is somewhere between 97.169 degrees Fahrenheit and 98.374 degrees Fahrenheit.<BR>\n" );
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