document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206798>Question 1206798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An important factor in selling a residential property is the number of people who look through the home. A sample of 11 homes recently sold in the Halifax, Nova Scotia, area revealed the mean number looking through each home was 17 and the standard deviation of the sample was 3 people. Develop a 90% confidence interval for the population mean. (Round the final answers to 2 decimal places.)\r<BR>\n" );
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document.write( "Confidence interval for the population mean is between <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844448 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=844448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "mu = population mean = unknown<BR>\n" );
document.write( "sigma = population standard deviation = unknown<BR>\n" );
document.write( "xbar = 17 = sample mean<BR>\n" );
document.write( "s = 3 = sample standard deviation<BR>\n" );
document.write( "n = 11 = sample size\r<BR>\n" );
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document.write( "Since we do not know the population standard deviation (sigma), and because n > 30 is not the case, we must use the T distribution.<BR>\n" );
document.write( "df = degrees of freedom<BR>\n" );
document.write( "df = n-1<BR>\n" );
document.write( "df = 11-1<BR>\n" );
document.write( "df = 10\r<BR>\n" );
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document.write( "At 90% confidence, and df = 10, the t critical value is roughly t =1.812\r<BR>\n" );
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document.write( "You can use a table such as this<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( "to determine the t critical value.<BR>\n" );
document.write( "Highlight the row that has df = 10. Highlight the column that has \"90%\" at the bottom. <BR>\n" );
document.write( "This row and column combo yields the value 1.812 which is approximate.\r<BR>\n" );
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document.write( "What this means is that P(-1.812 < t < 1.812) = 0.90 approximately when df = 10.\r<BR>\n" );
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document.write( "Another way to determine this t critical value is to use a stats calculator such as a TI84. <BR>\n" );
document.write( "The specific function to use on a TI84 is called invT.<BR>\n" );
document.write( "There are many other calculators that offer a similar feature.\r<BR>\n" );
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document.write( "Here are the important values we need<BR>\n" );
document.write( "t = 1.812 (approximate)<BR>\n" );
document.write( "xbar = 17<BR>\n" );
document.write( "s = 3<BR>\n" );
document.write( "n = 11\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "E = margin of error<BR>\n" );
document.write( "E = t*s/sqrt(n)<BR>\n" );
document.write( "E = 1.812*3/sqrt(11)<BR>\n" );
document.write( "E = 1.639016 approximately\r<BR>\n" );
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document.write( "L = lower bound of confidence interval<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 17 - 1.639016<BR>\n" );
document.write( "L = 15.360984<BR>\n" );
document.write( "L = <font color=red>15.36</font>\r<BR>\n" );
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document.write( "U = upper bound of confidence interval<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 17 + 1.639016<BR>\n" );
document.write( "U = 18.639016<BR>\n" );
document.write( "U = <font color=red>18.64</font>\r<BR>\n" );
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document.write( "The 90% confidence interval of the format (L, U) is roughly <font color=red>(15.36, 18.64)</font><BR>\n" );
document.write( "This represents <font color=red>15.36 < mu < 18.64</font> which is a more descriptive way of explaining what's going on (since it involves the parameter we're trying to estimate).\r<BR>\n" );
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document.write( "We are 90% confident that the population mean (mu) is somewhere between <font color=red>15.36 and 18.64</font><BR>\n" );
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