document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251242>Question 251242</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A corporate CEO reviews the earnings of three divisions over the last eighteen months.  Each division reports its earnings quarterly.  Based on the earnings below, is there sufficient evidence to conclude, at the 99% level of confidence, that one of these divisions is more profitable than the others?  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "Division I        <BR>\n" );
document.write( "45                <BR>\n" );
document.write( "33                <BR>\n" );
document.write( "22                <BR>\n" );
document.write( "50                <BR>\n" );
document.write( "18                <BR>\n" );
document.write( "59   \r<BR>\n" );
document.write( "\n" );
document.write( "Division II<BR>\n" );
document.write( "13<BR>\n" );
document.write( "27<BR>\n" );
document.write( "12<BR>\n" );
document.write( "17<BR>\n" );
document.write( "14<BR>\n" );
document.write( "7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Division III<BR>\n" );
document.write( "4<BR>\n" );
document.write( "18<BR>\n" );
document.write( "24<BR>\n" );
document.write( "19<BR>\n" );
document.write( "18<BR>\n" );
document.write( "8<BR>\n" );
document.write( "             <BR>\n" );
document.write( " <BR>\n" );
document.write( "•State the null and alternate hypotheses<BR>\n" );
document.write( "•Calculate the sums of squares SS(total), SS(factor), and SS(error)<BR>\n" );
document.write( "•Calculate the degrees of freedom df(total), df(factor), and df(error)<BR>\n" );
document.write( "•Calculate the mean square for factor, and the mean square for error<BR>\n" );
document.write( "•Calculate the F-statistic<BR>\n" );
document.write( "•Determine the critical value(s)<BR>\n" );
document.write( "•State your decision: Should the null hypothesis be rejected?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182987 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=182987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A corporate CEO reviews the earnings of three divisions over the last eighteen months. Each division reports its earnings quarterly. Based on the earnings below, is there sufficient evidence to conclude, at the 99% level of confidence, that one of these divisions is more profitable than the others? \r<BR>\n" );
document.write( "\n" );
document.write( "Division I <BR>\n" );
document.write( "45 <BR>\n" );
document.write( "33 <BR>\n" );
document.write( "22 <BR>\n" );
document.write( "50 <BR>\n" );
document.write( "18 <BR>\n" );
document.write( "59 <BR>\n" );
document.write( "Division II<BR>\n" );
document.write( "13<BR>\n" );
document.write( "27<BR>\n" );
document.write( "12<BR>\n" );
document.write( "17<BR>\n" );
document.write( "14<BR>\n" );
document.write( "7 \r<BR>\n" );
document.write( "\n" );
document.write( "Division III<BR>\n" );
document.write( "4<BR>\n" );
document.write( "18<BR>\n" );
document.write( "24<BR>\n" );
document.write( "19<BR>\n" );
document.write( "18<BR>\n" );
document.write( "8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "•State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: The means are equal<BR>\n" );
document.write( "H1: At least one of the means is different.<BR>\n" );
document.write( "----------------------------------------------------------<BR>\n" );
document.write( "I ran an ANOVA function on a TI-84 to get the following results:<BR>\n" );
document.write( "SS= 2070.3333<BR>\n" );
document.write( "MS= 1035.1667<BR>\n" );
document.write( "Error SS= 1825.6667<BR>\n" );
document.write( "Error MS= 121.7111<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "•Calculate the sums of squares <BR>\n" );
document.write( ".SS(total)= <BR>\n" );
document.write( ".SS(factor)<BR>\n" );
document.write( ".SS(error)\r<BR>\n" );
document.write( "\n" );
document.write( "•Calculate the degrees of freedom <BR>\n" );
document.write( "df(total), <BR>\n" );
document.write( "df(factor)= 2 <BR>\n" );
document.write( "and df(error)= 15<BR>\n" );
document.write( "•Calculate the mean square for factor, and the mean square for error<BR>\n" );
document.write( "•Calculate the F-statistic = 8.5051<BR>\n" );
document.write( "•Determine the critical value(s)<BR>\n" );
document.write( "•State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( "p-value: 0.0034<BR>\n" );
document.write( "Since the p-value is less than 5% reject Ho.<BR>\n" );
document.write( "=================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );