document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204280>Question 1204280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You intend to estimate a population mean  <BR>\n" );
document.write( "μ with the following sample.\r<BR>\n" );
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document.write( "24.7<BR>\n" );
document.write( "42.1<BR>\n" );
document.write( "36<BR>\n" );
document.write( "24.3<BR>\n" );
document.write( "-7.8<BR>\n" );
document.write( "32.2<BR>\n" );
document.write( "40.4\r<BR>\n" );
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document.write( "You believe the population is normally distributed. Find the 80% confidence interval. Enter your answer as an open-interval. This means enter your answer inside of parentheses accurate to two decimal places (because the sample data are reported accurate to one decimal place).<BR>\n" );
document.write( "For example if the lower limit is 12.23 and the upper limit is 15.34 enter your answer as (12.32,15.34)  \r<BR>\n" );
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document.write( "80% C.I. = \r<BR>\n" );
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document.write( "Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Did you enter your answer as an open-interval as described above? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840429 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is equal to 27.414285714286<BR>\n" );
document.write( "standard deviatiion is equal to 17.019736442478<BR>\n" );
document.write( "sample size is 7.<BR>\n" );
document.write( "t-score 80% confidence interval with 6 degrees of freedom = plus or minus t = 1.439755738.\r<BR>\n" );
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document.write( "i rounded intermediate values to 6 decimal places.<BR>\n" );
document.write( "that's more than enough detail for a final rounding of 2 or 3 decimal digits.\r<BR>\n" );
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document.write( "the rounded values used are:<BR>\n" );
document.write( "mean = 27.414286<BR>\n" );
document.write( "standard deviation = 17.019736<BR>\n" );
document.write( "degrees of freedom = sample size of 7 minus 1 = 6<BR>\n" );
document.write( "critical t-score = plus oe minus 1.439756\r<BR>\n" );
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document.write( "t-score formula used is t = (x - m) / s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard error\r<BR>\n" );
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document.write( "to solve for x, the formula bgecomes:<BR>\n" );
document.write( "x = s * t + m\r<BR>\n" );
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document.write( "standard error = standard deviation / sqrt(sample size).<BR>\n" );
document.write( "that is equal to 17.019736 / sqrt(7) = 6.432856\r<BR>\n" );
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document.write( "on the high side of the confidence interval, you get x = s * t + m becomes:<BR>\n" );
document.write( "x = 6.432856 * 1.439756 + 27.414286 = 36.676029.\r<BR>\n" );
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document.write( "on the low side of the confidence interval, you get x = s * t + m becomes:<BR>\n" );
document.write( "x = 6.432856 * -1.439756 + 27.414286 = 18.152543.\r<BR>\n" );
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document.write( "your solution is 80% confidence interval for the sample mean = (18.15,36.68).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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