document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205251>Question 1205251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quality controller of a company plans to inspect the average diameter of small bolts made. A random sample of 6 bolts was selected. The sample is computed to be 2.0016mm and the sample standard deviation 0.0012mm. Construct the 99% confidence interval for all bolts made. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841946 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=841946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 6.<BR>\n" );
document.write( "sample mean is 2.0016 millimeters.<BR>\n" );
document.write( "sample standard deviation is .0012 millimeters.\r<BR>\n" );
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document.write( "since the sample mean and sample standard deviation are used, then the 99% confidence interval will be based on the t-score, rather than the z-score.\r<BR>\n" );
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document.write( "99% two tail confidence interval for t-score with 5 degrees of freedom (degrees of freedom equal sample size minus 1) is equal to t = plus or minus 4.032142983.\r<BR>\n" );
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document.write( "since you're looking at a distribution of sample means for samples of 6 elements each, the standard error is used.<BR>\n" );
document.write( "standard error = standard deviation / sqrt(sample size) = .0012 / sqrt(6) = .0004898979486.\r<BR>\n" );
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document.write( "t-score formula is t = (x-m)/s<BR>\n" );
document.write( "t is the critical t-score<BR>\n" );
document.write( "x is the critical sample mean.<BR>\n" );
document.write( "m is the sample mean.<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "on the low side of the confidence interval, the t-score formula becomes:<BR>\n" );
document.write( "-4.032142983 = (x - 2.0016) / .0004898979486.<BR>\n" );
document.write( "solve for x to get x = 1.999624661.\r<BR>\n" );
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document.write( "on the high side of the confidence interval, the t-score formula becomes:<BR>\n" );
document.write( "4.032142983 = (x - 2.0016) / .0004898979486.<BR>\n" );
document.write( "solve for x to get x = 2.003575339.\r<BR>\n" );
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document.write( "your two tail 99% confidence interval is from 1.999624661 to 2.003575339.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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