document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203947>Question 1203947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A high school math teacher wants to assess the effectiveness of a new teaching method<BR>\n" );
document.write( "for improving students’ algebra skills. She selects a random sample of 8 students<BR>\n" );
document.write( "from her class and administers a pre-test to evaluate their algebra knowledge. After<BR>\n" );
document.write( "introducing the new teaching method over the course of a semester, she administers a<BR>\n" );
document.write( "post-test to the same students to measure any improvements in their algebra skills.<BR>\n" );
document.write( "Student 1 2 3 4 5 6 7 8<BR>\n" );
document.write( "Pre-Test Score 50 45 60 65 75 92 86 88<BR>\n" );
document.write( "Post-Test Score 52 50 65 62 71 90 89 90<BR>\n" );
document.write( "Construct a 95% confidence interval for the difference in means. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839925 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe this will require the use of a two sample paired t-test.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you find the differnces in the score of sample 2 minus sample 1 results for each student that participated.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used the calculator at <a  rel=nofollow HREF= \"https://www.mathportal.org/calculators/statistics-calculator/t-test-calculator.php\" target = \"_blank\">https://www.mathportal.org/calculators/statistics-calculator/t-test-calculator.php</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092911.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092912.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092913.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092914.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the procedures is to find the differences for each pair.<BR>\n" );
document.write( "then find the mean and the standard deviation of the distiribution of paired differnces.<BR>\n" );
document.write( "then calculate the standard error = standard deviation divided by square root of sample size.<BR>\n" );
document.write( "then do the t-test.<BR>\n" );
document.write( "then check the test t-score against the critical t-score.<BR>\n" );
document.write( "if it's greater, then the test results are significant and you conclude thre's a diference.<BR>\n" );
document.write( "if not, then you conclude that there is no difference.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the results of this test indicate that the results are not significant because the test t-score was less than the critical t-score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the conclusion is that the tests are not different and either test can be used.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference explaining how the paired t-test is done.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/paired-t-test.html\" target = \"_blank\">https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/paired-t-test.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );