document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202553>Question 1202553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A beer producer wants to find out whether its existing bottling equipment is working to standards. 151 bottles were selected for testing: the average beer fill level is x̄ = 50.1mm and the sample variance s^2 = 4mm^2.\r<BR>\n" );
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document.write( "Determine the 99% confidence interval for the mean value.<BR>\n" );
document.write( "Determine the 90% confidence interval for the variance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837463 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=837463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 151.<BR>\n" );
document.write( "sample mean is 50.1 millimeters.<BR>\n" );
document.write( "sample variance is 4 millimeters.<BR>\n" );
document.write( "sample standard deviation is square root of 4 = 2 millimeters.<BR>\n" );
document.write( "standard error is 2/sqrt(151) = 1.628 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "critical t-score at 99% two-tailed confidence inteval with 150 degrees of freedom is plus or minus 2.609 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "critical t-score at 90% two-tailed confidence interval with 150 degrees of freedom is plus or minus 1.656 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "mean of the sample is assumed to be 50.1.<BR>\n" );
document.write( "mean of the variance is assumed to be 4.\r<BR>\n" );
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document.write( "use the t-score formula to find the raw score of the confidence interval.<BR>\n" );
document.write( "formula is t = (x-m)/s<BR>\n" );
document.write( "t is the t-score.<BR>\n" );
document.write( "x is the critical raw score.<BR>\n" );
document.write( "m is the mean of the sample.<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "for the mean, the formula becomes:<BR>\n" );
document.write( "2.609 = (x - 50.1) / 1.628 on the high side.<BR>\n" );
document.write( "solve for x to get x = 2.609 * 1.628 + 50.1 = 54.35 rounded to 2 decimal places.<BR>\n" );
document.write( "-2.609 = (x - 50.1) / 1.628 on the low side.<BR>\n" );
document.write( "solve for x to get x = -2.609 * 1.628 + 50.1 = 45.85 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "for the variance, the formula becomes:<BR>\n" );
document.write( "1.656 = (x - 4) / 1.628 on the high side.<BR>\n" );
document.write( "solve for x to get x = 1.656 * 1.628 + 4 = 6.7 rounded to 2 decimal places.<BR>\n" );
document.write( "-1.656 = (x - 4) / 1.628 on the low side.<BR>\n" );
document.write( "solve for x to get x = -1.656 * 1.628 + 4 = 1.30 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "your 99% confidence interval for the mean is 45.85 to 54.35.<BR>\n" );
document.write( "your 99% confidence interval for the variance is 1.30 to 6.70.\r<BR>\n" );
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document.write( "i'm pretty sure about the mean of the sample.<BR>\n" );
document.write( "i think that's the way to analyze the variance of the sample, but i'm not surre.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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