document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181433>Question 1181433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assuming that the population standard deviation is unknown for a<BR>\n" );
document.write( "randomly selected sample whose size is 11, sketch the rejection region<BR>\n" );
document.write( "for a one-tailed test with 99% confidence. Does t = 2.86 fall in the<BR>\n" );
document.write( "rejection region? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811350 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=811350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you don't know the population standard deviation, then you're looking at a t-score with a sample size of 11 which gives you a t-score with  11 - 1 = 10 degrees of freedom.<BR>\n" );
document.write( "with a one-tailed test at 99% confidence level, the critical alpha on the right side of the distribution will be .01.<BR>\n" );
document.write( "the critical alpha is used to find the critical t-score.<BR>\n" );
document.write( "looking up a one tailed critical alpha of .01 in the critical t-score tables gets you a critical t-score of 2.764 with 10 degrees of freedom.<BR>\n" );
document.write( "your test t-score of 2.86 with 10 degrees of freedom would reside in the rejection region because it's greater than the critical t-score.<BR>\n" );
document.write( "my sketch looks like this.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/060501.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "any area to the right of the critical t-score is in the rejection zone.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the t-score table i used gives you the critical t-score with 10 degrees of freedom as shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/060502.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you choose one tailed alpha of .01 and then look for the corresponding t-score with 10 degrees of freedom.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your critical t-score based on the critical one teiled alpha.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can graph the t-score using the t-score graphinc calculator found at <a  rel=nofollow HREF= \"https://mathcracker.com/t-distribution-graph-generator#results\" target= \"_blank\">https://mathcracker.com/t-distribution-graph-generator#results</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graphs are shwn below.<BR>\n" );
document.write( "first graph is t-score of 2.764.<BR>\n" );
document.write( "second graph is t-score of 2.86.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the t-score of 2.86 is greater than the critical t-score of 2.764, you are in the rejection zone.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you are in the rejection zone, the test t-score of 2.86 give you a smaller area to the right of it as the critical z-score of 2.764.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the critical alpha is .01.<BR>\n" );
document.write( "the test alpha is .0085\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/060503.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/060504.jpg\">\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );