document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172028>Question 1172028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean length of certain bar for construction is supposed <BR>\n" );
document.write( "to be 43mm. There is a concern that the length has changed, <BR>\n" );
document.write( "12 bars were selected at random for a study. The following lengths were recorded: 44, 39, 45, 43, 40, 39, 41, 40, 42, 43, 42, 42 in mm. \r<BR>\n" );
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document.write( "Do you agree that there has been a change in the mean length? Use α= 1%<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 #796945 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=796945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is supposed to be 43.<BR>\n" );
document.write( "you find the mean of the sample to be equal to 41.66666<BR>\n" );
document.write( "you find the standard deviation of the sample to be 1.92275<BR>\n" );
document.write( "the sample size is 12 elements.<BR>\n" );
document.write( "the standard error is equal to the standard deviation of the sample divided by the sample size = 1.92275 / sqrt(12) = .55505<BR>\n" );
document.write( "the t-score with 11 degrees of freedom is equal to (41.66666 - 43) / .55505 = -2.40219.<BR>\n" );
document.write( "the area to the left of a t-score of -2.40219 with 11 degrees of freedom is equal to .017548.<BR>\n" );
document.write( "this is greater than .01 if a one tailed test, or .005 if a two tailed test.<BR>\n" );
document.write( "therefore, there is not enough evidence to determine that the actual mean is not 43.<BR>\n" );
document.write( "the difference is determined to be due to random variation in the mean of a sample of size 12.\r<BR>\n" );
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