document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394805>Question 394805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Do students at various universities differ in how sociable they are? Twenty-five<BR>\n" );
document.write( "students were randomly selected from each of three universities in a region and<BR>\n" );
document.write( "were asked to report on the amount of time they spent socializing each day with<BR>\n" );
document.write( "other students. The result for University X was a mean of 5 hours and an estimated<BR>\n" );
document.write( "population variance of 2 hours; for University Y,M = 4, S^2 = 1.5 ; and for University Z,M = 6, S^2 = 2.5<BR>\n" );
document.write( " . What should you conclude? Use the .05 level.<BR>\n" );
document.write( "(a) Use the steps of hypothesis testing, (b) figure the effect size for the study;<BR>\n" );
document.write( "and (c) explain your answers to parts (a) and (b) to someone who has never had<BR>\n" );
document.write( "a course in statistics. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280157 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: Ux=Uy=Uz<BR>\n" );
document.write( "Ha: not all are equal<BR>\n" );
document.write( "-<BR>\n" );
document.write( "compute the sum squares for between groups x,y,z<BR>\n" );
document.write( "SSB=sum(ni*(Xi-Xbar)^2) where ni=sample size for group i, Xi=sample average for group i, and Xbar=overall average.<BR>\n" );
document.write( "ni=25 for each group,  Xx=5,Xy=4,Xz=6, Xbar=5<BR>\n" );
document.write( "SSB=25*(0^2+(-1)^2+1^2)=50<BR>\n" );
document.write( "degrees of freedom= k-1=3-1=2, k=number of groups<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Compute the sum squares for the error<BR>\n" );
document.write( "SSE=sum((ni-1)*Si^2)=24*(2+1.5+2.5)=144<BR>\n" );
document.write( "degrees of freedom= k(ni-1)=3(25-1)=3*24=72, k=number of groups<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Compute Mean sum of squares for between groups and error<BR>\n" );
document.write( "MSB=SSB/dof=50/2=25<BR>\n" );
document.write( "MSE=SSE/dof=144/72=2<BR>\n" );
document.write( "--<BR>\n" );
document.write( "compute F statistic= MSB/MSE=25/2=12.5<BR>\n" );
document.write( "--<BR>\n" );
document.write( "determine the critical F value for alpha 0.05, num dof=2, denom dof=72<BR>\n" );
document.write( "Fcritical= 3.12<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Since Fstatistic > Fcritical then reject Ho and conclude<BR>\n" );
document.write( "The universities differ in their average time socializing\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );