document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169528>Question 1169528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> n=10 <BR>\n" );
document.write( "x=755<BR>\n" );
document.write( "y=819<BR>\n" );
document.write( "xy=62085<BR>\n" );
document.write( "x^2=68025<BR>\n" );
document.write( "y^2=68109\r<BR>\n" );
document.write( "\n" );
document.write( "If the level of significance is 0.01 and r=0.24 how to compute test statistic? (step 3 in correlation process) <BR>\n" );
document.write( "Test Statistic:n=?  __?__ -test<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 #851313 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down how to compute the test statistic for a correlation coefficient.\r<BR>\n" );
document.write( "\n" );
document.write( "**Understanding the Problem**\r<BR>\n" );
document.write( "\n" );
document.write( "We are given:\r<BR>\n" );
document.write( "\n" );
document.write( "* $n = 10$ (sample size)<BR>\n" );
document.write( "* $r = 0.24$ (correlation coefficient)<BR>\n" );
document.write( "* Significance level ($\alpha$) = 0.01\r<BR>\n" );
document.write( "\n" );
document.write( "We need to calculate the test statistic for the correlation coefficient.\r<BR>\n" );
document.write( "\n" );
document.write( "**Formula for the Test Statistic**\r<BR>\n" );
document.write( "\n" );
document.write( "The test statistic for a correlation coefficient is calculated using the following formula:\r<BR>\n" );
document.write( "\n" );
document.write( "$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$\r<BR>\n" );
document.write( "\n" );
document.write( "**Step-by-Step Calculation**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Calculate $r^2$:**<BR>\n" );
document.write( "    $$r^2 = (0.24)^2 = 0.0576$$\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Calculate $1 - r^2$:**<BR>\n" );
document.write( "    $$1 - r^2 = 1 - 0.0576 = 0.9424$$\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Calculate $\sqrt{1 - r^2}$:**<BR>\n" );
document.write( "    $$\sqrt{1 - r^2} = \sqrt{0.9424} \approx 0.97077$$\r<BR>\n" );
document.write( "\n" );
document.write( "4.  **Calculate $\sqrt{n - 2}$:**<BR>\n" );
document.write( "    $$\sqrt{n - 2} = \sqrt{10 - 2} = \sqrt{8} \approx 2.8284$$\r<BR>\n" );
document.write( "\n" );
document.write( "5.  **Calculate $r\sqrt{n - 2}$:**<BR>\n" );
document.write( "    $$r\sqrt{n - 2} = 0.24 \times 2.8284 \approx 0.6788$$\r<BR>\n" );
document.write( "\n" );
document.write( "6.  **Calculate the test statistic $t$:**<BR>\n" );
document.write( "    $$t = \frac{0.6788}{0.97077} \approx 0.6992$$\r<BR>\n" );
document.write( "\n" );
document.write( "**Result**\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the test statistic is approximately 0.6992.\r<BR>\n" );
document.write( "\n" );
document.write( "**Final Answer**\r<BR>\n" );
document.write( "\n" );
document.write( "Test Statistic: n=10 t-test = 0.6992<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );