document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380865>Question 380865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether a correlation coefficient of r = -0.405 is significant at 5% level for a sample size of 22.  r is not sifnificant at 5% or  r is significant at 5% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270291 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=270291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the t-distribution for small samples. <BR>\n" );
document.write( "The test statistic is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+r%2Asqrt%28%28n-2%29%2F%281-r%5E2%29%29 ALIGN=MIDDLE  ALT=\"t+=+r%2Asqrt%28%28n-2%29%2F%281-r%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+r%2Asqrt%2820%2F%281-%28-0.405%29%5E2%29%29+=+-1.98 ALIGN=MIDDLE  ALT=\"t+=+r%2Asqrt%2820%2F%281-%28-0.405%29%5E2%29%29+=+-1.98\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Degree of freedom is 22- 2 = 20. <BR>\n" );
document.write( "For 20 df and one-tailed test, critical value is -1.725.  Since -1.725 > -1.98, r is significant at the 5% level. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );