document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058361>Question 1058361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sample size of A = 10<BR>\n" );
document.write( "Sample mean of A = 29.5<BR>\n" );
document.write( "Sample Standard Deviation of A = 0.7\r<BR>\n" );
document.write( "\n" );
document.write( "Sample size of B = 9<BR>\n" );
document.write( "Sample mean of B = 30.3<BR>\n" );
document.write( "Sample Standard Deviation of B = 0.5\r<BR>\n" );
document.write( "\n" );
document.write( "Normally distributed random variables.\r<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >=0.05\r<BR>\n" );
document.write( "\n" );
document.write( "Is the variability of A significantly different from B?\r<BR>\n" );
document.write( "\n" );
document.write( "Is the mean of A significantly different from B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673422 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start with the difference in means first.<BR>\n" );
document.write( "Null Hypothesis-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ho ALIGN=MIDDLE  ALT=\"Ho\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5BA%5D=u%5BB%5D ALIGN=MIDDLE  ALT=\"u%5BA%5D=u%5BB%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5BA%5D=u%5BB%5D ALIGN=MIDDLE  ALT=\"u%5BA%5D=u%5BB%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Alternate Hypothesis-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ha ALIGN=MIDDLE  ALT=\"Ha\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5BA%5D%3C%3Eu%5BB%5D ALIGN=MIDDLE  ALT=\"u%5BA%5D%3C%3Eu%5BB%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=0.05 ALIGN=MIDDLE  ALT=\"alpha=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use unpooled standard deviation method,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2829.5-30.3%29%2Fsqrt%280.7%5E2%2F10%2B0.5%5E2%2F9%29=-2.887+ ALIGN=MIDDLE  ALT=\"t=%2829.5-30.3%29%2Fsqrt%280.7%5E2%2F10%2B0.5%5E2%2F9%29=-2.887+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=+%28%280.7%29%5E2%2F10%29%2F%28%280.7%29%5E2%2F10%2B%280.5%29%5E2%2F9%29=0.6382+ ALIGN=MIDDLE  ALT=\"C=+%28%280.7%29%5E2%2F10%29%2F%28%280.7%29%5E2%2F10%2B%280.5%29%5E2%2F9%29=0.6382+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DOF=%28%2810-1%29%289-1%29%29%2F%28%289-1%29%280.6238%29%2B%281-0.6238%29%5E2%2810-1%29%29=11.494 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rounding down,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DOF=11 ALIGN=MIDDLE  ALT=\"DOF=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Checking the critical t value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DOF=11 ALIGN=MIDDLE  ALT=\"DOF=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=0.05 ALIGN=MIDDLE  ALT=\"alpha=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bc%5D=-2.201 ALIGN=MIDDLE  ALT=\"t%5Bc%5D=-2.201\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%3Ct%5Bc%5D ALIGN=MIDDLE  ALT=\"t%3Ct%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, reject the null hypothesis. <BR>\n" );
document.write( "The sample means are significantly different.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "With regards to the variances, are you supposed to use a particular test to check. F test?<BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=s%5B1%5D%5E2%2Fs%5B2%5D%5E2=%280.7%2F0.5%29%5E2=1.96 ALIGN=MIDDLE  ALT=\"F=s%5B1%5D%5E2%2Fs%5B2%5D%5E2=%280.7%2F0.5%29%5E2=1.96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I used EXCEL with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=1.96 ALIGN=MIDDLE  ALT=\"X=1.96\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DOF%5B1%5D=9 ALIGN=MIDDLE  ALT=\"DOF%5B1%5D=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DOF%5B2%5D=8 ALIGN=MIDDLE  ALT=\"DOF%5B2%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get a p value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.356 ALIGN=MIDDLE  ALT=\"0.356\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.356%3E0.05 ALIGN=MIDDLE  ALT=\"0.356%3E0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is no significant difference between the samples using the variances.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );