document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136460>Question 1136460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The human resources department of a consulting firm gives a standard creativity test to a randomly selected group of <BR>\n" );
document.write( "new hires every year. This year, 65 new hires took the test and scored a mean of 112.8 points with a standard deviation of 15.6. Last year, <BR>\n" );
document.write( " 90 new hires took the test and scored a mean of 117.2 points with a standard deviation of. Assume that the population standard deviations of 17.2 the test scores of all new hires in the current year <BR>\n" );
document.write( "and the test scores of all new hires last year can be estimated by the sample standard deviations, as the <BR>\n" );
document.write( "samples used were quite large. Construct a 95% confidence interval for u1-u2, the difference between the mean test <BR>\n" );
document.write( "score u1 of new hires from the current year and the mean test score u2 of new hires from last year. Then <BR>\n" );
document.write( "complete the table below.<BR>\n" );
document.write( "Carry your intermediate computations to at least three decimal places. <BR>\n" );
document.write( "Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)\r<BR>\n" );
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document.write( "What is the lower limit of the 95% confidence interval?\r<BR>\n" );
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document.write( "What is the upper limit of the 95% confidence interval?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754224 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There needs to be clarification of<BR>\n" );
document.write( "1. What is the sd of the 90 hires?<BR>\n" );
document.write( "2. This should be a 2-sample t-test given that s is being used to estimate sigma.  Where does the \"population standard deviation\" come from?  Is s of the prior year 17.2?\r<BR>\n" );
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document.write( "half-interval is t*(sp*sqrt((1/n1)+(1/n2)))\r<BR>\n" );
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document.write( "If I can assume the sd of the prior year for 17.2, and that was a sample, <BR>\n" );
document.write( "then sp^2=(n1-1)s1^2+(n2-2)s2^2/(n1+n2-2)<BR>\n" );
document.write( "sp^2=64*15.6^2+89*17.2^2/(153)<BR>\n" );
document.write( "sp^2=273.888; sp=16.550<BR>\n" );
document.write( "t df=153,0.975=1.976<BR>\n" );
document.write( "difference in means is -4.40<BR>\n" );
document.write( "denominator of (sqrt ((1/n1)+(1/n2)))=0.02650; sp*sqrt((1/n1)+(1/n2))=2.694.<BR>\n" );
document.write( "Multiply that by t of 1.976 to get 5.32<BR>\n" );
document.write( "interval is (-9.72, 0.82)\r<BR>\n" );
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document.write( "(0 is in the interval so it would not be significant)\r<BR>\n" );
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