document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203978>Question 1203978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:\r<BR>\n" );
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document.write( "Summary<BR>\n" );
document.write( "Groups	Sample Size	Sum	Average	Variance<BR>\n" );
document.write( "Line A	6	250	41.66667	0.266667<BR>\n" );
document.write( "Line B	6	260	43.33333	0.666667<BR>\n" );
document.write( "Line C	6	249	41.5	0.7<BR>\n" );
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document.write( "ANOVA<BR>\n" );
document.write( "Source of Variation	SS	df	MS	F	p-value<BR>\n" );
document.write( "Between Groups	12.33333	2	6.166667	11.32653	0.001005<BR>\n" );
document.write( "Within Groups	8.166667	15	0.544444	 	 <BR>\n" );
document.write( "Total	20.5	17	 	 	 \r<BR>\n" );
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document.write( "Compute 99% confidence intervals that estimate the difference between each pair of means. (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places.) Which pairs of means are statistically different? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839960 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=839960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i found a calculator online at <a  rel=nofollow HREF= \"https://statpages.info/anova1sm.html\" target = \"_blank\">https://statpages.info/anova1sm.html</a>that does the analysis you are looking for.<BR>\n" );
document.write( "it works off the mean and the standard deviation, i.e. uses summarized data.<BR>\n" );
document.write( "i used the summarized data you had and got similar results.<BR>\n" );
document.write( "this indicates to me that the results were consistent with what you got.<BR>\n" );
document.write( "it also does the sample to sample posthoc analysis.<BR>\n" );
document.write( "the results as shown below.\r<BR>\n" );
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document.write( "group 1 was line A<BR>\n" );
document.write( "group 2 was line B<BR>\n" );
document.write( "group 3 was line C.\r<BR>\n" );
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document.write( "the results indicate that line A to line B are statistically different from each other because the p-value was .0037 which is less than .01.\r<BR>\n" );
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document.write( "standard deviation = square root of variance, so i took the square root of the variance given and used that as input to the calculator.<BR>\n" );
document.write( "i round to 6 decimal digits which is usually enough for accurate readings.\r<BR>\n" );
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