document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204650>Question 1204650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	The nine items of a sample had the following values: 45, 47, 50, 52, 48, 47, 49, 53, 51. Does the mean of the nine items differ significantly from the assumed population mean 47.5? (a = 0.05) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841043 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=841043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the mean and standad deviation of the sample.<BR>\n" );
document.write( "i get meqan = 49.1111 and standard deviation = 2.6914<BR>\n" );
document.write( "standard error = standard deviation / sqrt(sample size) = 2.6914 / sqrt(9) = .8971<BR>\n" );
document.write( "t-score = (x-m)/s = (49.1111 - 47.5) / .8971 = 1.7959.<BR>\n" );
document.write( "area under normal distributuion curve to the right of that t-score with 8 degrees of freedom = .0551<BR>\n" );
document.write( "two tailed critical p-factor on each end of 95% confidence interval = .025.<BR>\n" );
document.write( "this is higher than that, indicating the resuls are not significant.<BR>\n" );
document.write( "there is not enough information to say that the population mean is not what is claimed to be.<BR>\n" );
document.write( "i solved this with my ti-84 plus calculator and confirmed the answer through the use of the online statistical calculator at <a  rel=nofollow HREF= \"https://www.statskingdom.com/130MeanT1.html\" target = \"_blank\">https://www.statskingdom.com/130MeanT1.html</a><BR>\n" );
document.write( "here are the results from that calculator.\r<BR>\n" );
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document.write( "the results indicae that the p-value is 10.22.<BR>\n" );
document.write( "the p-value i got from my ti-84 plus was .0511.<BR>\n" );
document.write( "the .0511 p-value i got was for the high end tail of the confidence interval.<BR>\n" );
document.write( "that would be alpha/2.<BR>\n" );
document.write( "alpha is therefore twice that = 10.22<BR>\n" );
document.write( "the critical alpha is .05 on both tails.<BR>\n" );
document.write( "that's .025 for each tail.<BR>\n" );
document.write( "when comparing p-values, you would either compare .0511 to .025 or .1022 to .05.<BR>\n" );
document.write( "either way, the test p-value is higher than the critical p-value by a fairly wide margin.<BR>\n" );
document.write( "the results from the online calculator tell you that the 95% confidence interval is 47.0977 to 51.1245.<BR>\n" );
document.write( "49.1111 is within tht interval, indicating the results are not significant at .05 two tailed significance level.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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