document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173384>Question 1173384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question :<BR>\n" );
document.write( "A sample of 49 is drawn from a normal population with unknown mean and variance. If the sample means is 131.8 and standard deviation 6.25,setup a 90% confidence  interval for the population mean?\r<BR>\n" );
document.write( "\n" );
document.write( "PLEASE REQUIRED DETAILED ANSWER:<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 #798765 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=798765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 49<BR>\n" );
document.write( "mean of sample is 131.8<BR>\n" );
document.write( "standard deviation of sample is 6.25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to set up a 90% confidence interval.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "degrees of freedom is 49 - 1 = 48.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = standard deviation of sample divided by square root of sample size.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you will be using t-scores with 48 degrees of freedom.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = 6.25 / sqrt(49) = 6.25 / 7 = .8928571429.<BR>\n" );
document.write( "i rounded this to .892857 which is probability a little more than close enouogh.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the t-score table, with 90% confidence interval, one tailed alpha would be 5% and two tailed alpha would be 10% (5% on each end).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's the table i used.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\" target = \"_blank\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that table only showed degrees of freedom of 40 and 60.<BR>\n" );
document.write( "48 degrees of freedom is somewhere in between.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "fortunately, there is a t-score calculator online that can be used to get more accurate critical t-score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that t-score calculator can be found at <a  rel=nofollow HREF= \"https://stattrek.com/online-calculator/t-distribution.aspx\" target = \"_blank\">https://stattrek.com/online-calculator/t-distribution.aspx</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the calculator gets you the area to the left of the t-score.<BR>\n" );
document.write( "to find the two tailed 10% conidence interval, i entered .05 in the p(T < t) box and a mean of 0 and a standard deviatiion of 1 and degrees of freedom of 48 and clicked on calculate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "calculator said the t-score was -1.677<BR>\n" );
document.write( "since the normal distribution table is symmetric, my confidence interval would be between a t-score of -1.677 and a t-score of 1.677<BR>\n" );
document.write( "that would be 5% area to the left of -1.677 and 5% area to the right of -1.677.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the table, two tailed of 10% with 40 degrees of freedom gave a t-score of -1.684 and 60 degrees of freedom gave a t-score of 1.671.<BR>\n" );
document.write( "about halfway between those t-score would yield a t-score of -1.6775 which is pretty close to -1.677 found by the calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used a critical t-score of plus or minus 1.677 for my 10% two tailed confidence interval.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "once this is done, you need to use the t-score formula to find the raw score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t-score formula is t = (x - m) / s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for t = -1.677, i got:<BR>\n" );
document.write( "-1.677 = (x - 131.8) / .892857 <BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = -1.677 * .892857 + 131.8 = 130.3026788\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for t = 1.677, i got:<BR>\n" );
document.write( "1.677 = (x - 131.8) / .892857<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1.677 * .892857 + 131.8 = 133.2973212\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answer should be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "90% confidence interval is between 130.3026788 and 133.2973212.\r<BR>\n" );
document.write( "<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" );