document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194299>Question 1194299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following are measurements of the heat-producing capacity (in millions of calories per ton) of random samples of five specimens each of coal from two mines:<BR>\n" );
document.write( "Mine 1: 8,380 8,210 8,360 7,840 7,910 Mine 2: 7,540 7,720 7,750 8,100 7,690<BR>\n" );
document.write( "Use the 0.05 level of significance to test whether the difference between the means of these two samples is significant.<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 #826506 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean M1=8140 with s1=251.9<BR>\n" );
document.write( "mean M2=7760 with s2=206.5<BR>\n" );
document.write( "sp=(s1^2+s2^2)/2<BR>\n" );
document.write( "=230.32<BR>\n" );
document.write( "Ho: means equal<BR>\n" );
document.write( "Ha; they aren't equal<BR>\n" );
document.write( "alpha=0.05 p{reject Ho|Ho true)<BR>\n" );
document.write( "test is a t (0.975 df=8)<BR>\n" );
document.write( "critical value is |t|>2.306<BR>\n" );
document.write( "t=380/230.3*sqrt(1/5+1/5)=380/145.84<BR>\n" );
document.write( "t=2.61, which is greater than the critical value, so reject Ho and conclude there is a difference at the 0.05 level.<BR>\n" );
document.write( "p-value =0.03.<BR>\n" );
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