document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206223>Question 1206223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A sample of 65 observations select from a somewhat normal population gave a mean of 2.67 with standard deviation of 0.75. <BR>\n" );
document.write( "A sample of 50 observations was independently taken from normal distribution and the mean was 2.59 with standard deviation of 0.66<BR>\n" );
document.write( "A. If the objective is to make a comparison of the mean of the two populations, which method is <BR>\n" );
document.write( "appropriate and why?<BR>\n" );
document.write( "B. Test whether the first population has greater mean as compared to the second. What is your conclusion at 5% level of significance?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843582 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=843582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample 1 has 65 observations with a mean of 2.67 and a standard deviation of .75.<BR>\n" );
document.write( "sample 2 has 50 observations with a mean of 2.59 and a standard deviation of .66.\r<BR>\n" );
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document.write( "it looks like a two sample t-test would be appropriate for this.\r<BR>\n" );
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document.write( "test is to see if sample 1 mean is greater than sample 2 mean.<BR>\n" );
document.write( "level of significance is .05.<BR>\n" );
document.write( "it is one tail with the level of significant on the right side of the confidence interval.\r<BR>\n" );
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document.write( "i used the two sample t-test calculator at <a  rel=nofollow HREF= \"https://www.statskingdom.com/140MeanT2eq.html\" target = \"_blank\">https://www.statskingdom.com/140MeanT2eq.html</a>\r<BR>\n" );
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document.write( "inputs and results of the analysis are shown below.\r<BR>\n" );
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document.write( "inuts:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/022601.jpg\">\r<BR>\n" );
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document.write( "results:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/022602.jpg\">\r<BR>\n" );
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document.write( "at .05 right tail level of significance, critical  t-score with 113 degrees of freedom would be equal to 1.66.\r<BR>\n" );
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document.write( "right tail critical p-value is .05.\r<BR>\n" );
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document.write( "the test t-score was .597<BR>\n" );
document.write( "the test p-value was .2758\r<BR>\n" );
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document.write( "since the test t-score was less than the critical t-score, the results were not significant.<BR>\n" );
document.write( "likewise, since the test p-value was greater than the critical p-value, the results were not significant.<BR>\n" );
document.write( "these results are always consistent with each other, i.e. both significant or both not significant conclusions.\r<BR>\n" );
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document.write( "the graph shows that the test t-score are clearly within the confidence interval.\r<BR>\n" );
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document.write( "the conclusion is that there is not sufficient information to conclude that the first population mean was greater than the second population mean.<BR>\n" );
document.write( "the population means are considered to be the same with differences due to normally expected variation in sample means.\r<BR>\n" );
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document.write( "the two sample t-test was used instead of the two sample z-test because the standard deviations were taken fom the samples and not from the population.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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