document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189908>Question 1189908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To compare the results of boys and girls in a class, a special test was given to 50 boys who averaged 67.4 with standard deviation of 5, and 50 girls averaged 62.8 with standard deviation of 4.6 <BR>\n" );
document.write( "a) Test, at alpha=0.05, whether the difference is significant or not.<BR>\n" );
document.write( "b) Test if the difference is 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821430 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=821430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: mu boy=mu girl<BR>\n" );
document.write( "Ha: mu boy NE mu girl<BR>\n" );
document.write( "alpha=0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "test is 2 sample t-test<BR>\n" );
document.write( "df=98<BR>\n" );
document.write( "critical value is 1.985<BR>\n" );
document.write( "calculation t=(diff means/SE)<BR>\n" );
document.write( "=(67.4-62.8)/sqrt (s1^2/n1)+(s2^2/n2))<BR>\n" );
document.write( "=4.6/sqrt [(25/50+(21.16/50)]<BR>\n" );
document.write( "=4.6/.96=4.79<BR>\n" );
document.write( "reject Ho and conclude there is a difference between the two at the 0.05 level.<BR>\n" );
document.write( "p-value <0.0001<BR>\n" );
document.write( "-<BR>\n" );
document.write( "For difference of 3,<BR>\n" );
document.write( "mu boy-mu girl <=3<BR>\n" );
document.write( "mu boy-mu girl NE>=3<BR>\n" );
document.write( "t-value is 3/0.96=3.125, so reject that hypothesis and say that the difference is greater than 3. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );