document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158759>Question 1158759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you want to test the claim that μ ≠ 3.5. Given a sample size of n = 40 and a level of α=0.05 when should you reject H 0 ?<BR>\n" );
document.write( "A)Reject H0 if the standardized test statistic is greater than 1.645 or less than -1.645<BR>\n" );
document.write( "B)Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575<BR>\n" );
document.write( "C)Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33.<BR>\n" );
document.write( "D)Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96.\r<BR>\n" );
document.write( "\n" );
document.write( "This should be a two-tailed test, with the critical values at the α = 0.05 level of significance and n  -  1 =39 degrees of freedom. The T Value calculator showed the T-Value (two-tailed)to be +/- 2.022691. I don't think I'm doing this right...<BR>\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 #781740 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=781740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: D) Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We don't need to know the standard deviation as all we're worrying about are the boundaries to the rejection regions and the acceptance region. In other words, we aren't calculating the test statistic here. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We want to know the value of k such that P(-k < Z < k) = 0.95<BR>\n" );
document.write( "The 0.95 is from 1-alpha = 1-0.05 = 0.95 which is the confidence level\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using a calculator or a Z table will show k = 1.96 approximately\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because n = 40 is larger than 30, this means we can use a standard normal Z distribution to approximate the T distribution. So we won't be using the T distribution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A way to rephrase choice D is to say \"Reject H0 if the standardized test statistic is not between -1.96 and 1.96\"<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );