document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207317>Question 207317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a population that I ran the mean for and got   55.1 as the Central measure of 10,000 data points.<BR>\n" );
document.write( "Then I took 25 data points per sample and generated the sample means ( Actually ran 100 samples but I will sample the sample )<BR>\n" );
document.write( "Here they are. Using Central Limit theorem concept, prove or disprove it by verifying the sample means approximate the population mean<BR>\n" );
document.write( "to the ( at least ) 95% level of confidence\r<BR>\n" );
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document.write( "Sample means:  55.2,  55.7,  54.8,  54.9,  55.2,  55.3,  54.8,  55.1,  55.4,  54.6,  54.8,  55.2,  55.0,  54.9,  54.8,  55.0,  54.3 \r<BR>\n" );
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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 #156877 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have a population that I ran the mean for and got 55.1 as the Central measure of 10,000 data points.<BR>\n" );
document.write( "Then I took 25 data points per sample and generated the sample means ( Actually ran 100 samples but I will sample the sample )<BR>\n" );
document.write( "Here they are. Using Central Limit theorem concept, prove or disprove it by verifying the sample means approximate the population mean<BR>\n" );
document.write( "to the ( at least ) 95% level of confidence <BR>\n" );
document.write( "Sample means: 55.2, 55.7, 54.8, 54.9, 55.2, 55.3, 54.8, 55.1, 55.4, 54.6, 54.8, 55.2, 55.0, 54.9, 54.8, 55.0, 54.3 <BR>\n" );
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document.write( "According to the CLT the mean of the sample means you have listed should<BR>\n" );
document.write( "approach the mean of the population as the number of sample means increases,<BR>\n" );
document.write( "and the standard deviation of the sample means should approach the quotient<BR>\n" );
document.write( "of the population standard deviation and the sqrt(sample size) under the<BR>\n" );
document.write( "same restriction.<BR>\n" );
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document.write( "The mean of your sample means can be gotten by adding the sample means<BR>\n" );
document.write( "you have listed and dividing by the number of sample means you have.<BR>\n" );
document.write( "I get mean of sample means = 55 and standard deviation of the <BR>\n" );
document.write( "sample means is 0.3260<BR>\n" );
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document.write( "Ho: u(sample means) = 55.1<BR>\n" );
document.write( "Ha: u(sample means) is not 55.1<BR>\n" );
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document.write( "alpha = 5%<BR>\n" );
document.write( "I ran a T-test and got the following:<BR>\n" );
document.write( "test statistic: t = -1.2649..<BR>\n" );
document.write( "p-value = 0.224...<BR>\n" );
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document.write( "Conclusion: Since the p-value is greater than alpha=5%, Fail to <BR>\n" );
document.write( "Reject Ho.<BR>\n" );
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document.write( "Conclusion: The test results support the claim of the CLT<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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