document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120294>Question 1120294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #18<BR>\n" );
document.write( "Test the claim that the mean GPA of night students is smaller than 2.1 at the 0.005 significance level.\r<BR>\n" );
document.write( "\n" );
document.write( "The null and alternative hypothesis would be:\r<BR>\n" );
document.write( "\n" );
document.write( "H0:&#956;&#8804;2.1 and H1:&#956;>2.1<BR>\n" );
document.write( "or<BR>\n" );
document.write( "H0:p=0.525 and H1:p&#8800;0.525<BR>\n" );
document.write( "or<BR>\n" );
document.write( "H0:&#956;&#8805;2.1 and H1:&#956;<2.1<BR>\n" );
document.write( "or<BR>\n" );
document.write( "H0:p&#8805;0.525 and H1:p<0.525<BR>\n" );
document.write( "or<BR>\n" );
document.write( "H0:p&#8804;0.525 and H1:p>0.525<BR>\n" );
document.write( "or<BR>\n" );
document.write( "H0:&#956;=2.1 and H1:&#956;&#8800;2.1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The test is:\r<BR>\n" );
document.write( "\n" );
document.write( "   right-tailed<BR>\n" );
document.write( "or left-tailed<BR>\n" );
document.write( "or two-tailed\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Based on a sample of 65 people, the sample mean GPA was 2.06 with a standard deviation of 0.08\r<BR>\n" );
document.write( "\n" );
document.write( "The p-value is:_______ (to 2 decimals)\r<BR>\n" );
document.write( "\n" );
document.write( "Based on this we:\r<BR>\n" );
document.write( "\n" );
document.write( "    Reject the null hypothesis<BR>\n" );
document.write( " or   Fail to reject the null hypothesis\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 #736023 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=736023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Because the question asks for a single directional answer, this is a one-way test.  Hypothesis testing is about parameters, not statistics.<BR>\n" );
document.write( "It is the third,<BR>\n" );
document.write( "Ho: mu >=2.1 and Ha: mu < 2.1<BR>\n" );
document.write( "The rejection region will be in the left tail, so a left tail test.<BR>\n" );
document.write( "Test stat is a t 0.005, df=64, critical value is t<-2.65<BR>\n" );
document.write( "t=(x-mean)/s/sqrt(n)<BR>\n" );
document.write( "=-0.05/0.08/sqrt(65)<BR>\n" );
document.write( "This is -0.05*sqrt(65)/0.08, or -5.039, Reject Ho<BR>\n" );
document.write( "p-value <0.0001 or <0.01<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );