document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=844710>Question 844710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of n = 16 individuals is selected from a population with &#956; = 70, and a treatment is administered to each individual in the sample.  After treatment, the sample mean is found to be M = 76 with SS = 960.\r<BR>\n" );
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document.write( "a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)\r<BR>\n" );
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document.write( "b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M (Note: In a hypothesis test, this value is the denominator of the t statistic.)\r<BR>\n" );
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document.write( "c. Based on sample data, does the treatment have a significant effect? Use a two-tailed test with &#945; = .05\r<BR>\n" );
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document.write( "What is the decision for parts a,b,and c? How would I report them in A.P.A. format?\r<BR>\n" );
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document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508907 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=508907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A random sample of n = 16 individuals is selected from a population with &#956; = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 76 with SS = 960. <BR>\n" );
document.write( "a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)<BR>\n" );
document.write( "Ans: 76-70 = 6<BR>\n" );
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document.write( "b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M (Note: In a hypothesis test, this value is the denominator of the t statistic.)<BR>\n" );
document.write( "Ans: 960/sqrt(16) = 240<BR>\n" );
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document.write( "c. Based on sample data, does the treatment have a significant effect? Use a two-tailed test with &#945; = .05 <BR>\n" );
document.write( "t(76) = (76-70)/240 = 6/240 = 1/40<BR>\n" );
document.write( "p-value = 2*P(t > 1/40 when df = 15) = 2tcdf(1/40,100,15) = 0.49<BR>\n" );
document.write( "Since the p-value is greater than 5%, fail to reject Ho.<BR>\n" );
document.write( "Conclusion: The test results does not support the claim that the <BR>\n" );
document.write( "population mean is 70.<BR>\n" );
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document.write( "What is the decision for parts a,b,and c? How would I report them in A.P.A. format? <BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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