document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523804>Question 523804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The SAT Quantitative Test has a population mean of 500 and a population standard deviation of 100.  Suppose you randomly select a sample of 25 participants and administer the SAT Quantitative Test to each participant.\r<BR>\n" );
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document.write( "			a.	What would you expect the mean of this sample to be?  	_________________\r<BR>\n" );
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document.write( "			b.	What is the standard error of the mean for samples of size 25 from this population?						<BR>\n" );
document.write( "											____________________\r<BR>\n" );
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document.write( "			c.	What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score greater than 530?<BR>\n" );
document.write( "											____________________\r<BR>\n" );
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document.write( "			d.	What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score	less than 480?<BR>\n" );
document.write( "											____________________\r<BR>\n" );
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document.write( "			e.	What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score between 485 and 525?\r<BR>\n" );
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document.write( "											_____________________\r<BR>\n" );
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document.write( "			f.	Suppose we obtain a mean SAT Quantitative Score of 515.  What is the 95% confidence interval for these data?<BR>\n" );
document.write( "											_____________________\r<BR>\n" );
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document.write( "			g.	Supposed we obtain a mean SAT Quantitative Score of 487.  What is the 80% confidence interval for these data?<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 #347464 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=347464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The SAT Quantitative Test has a population mean of 500 and a population standard deviation of 100. <BR>\n" );
document.write( "Suppose you randomly select a sample of 25 participants and administer the SAT Quantitative Test to each participant.<BR>\n" );
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document.write( "a. What would you expect the mean of this sample to be?:::500<BR>\n" );
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document.write( "b. What is the standard error of the mean for samples of size 25 from this population?:::100/sqrt(25) = 20<BR>\n" );
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document.write( "c. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score greater than 530?<BR>\n" );
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document.write( "t(530) = (530-500)/20 = 3/2<BR>\n" );
document.write( "P(x-bar) = P(t > 3/2 when df = 24) = 0.0733<BR>\n" );
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document.write( "d. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score less than 480?<BR>\n" );
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document.write( "t(480) = (480-500)/20 = -1<BR>\n" );
document.write( "P(x-bar > 480) = P(t < -1 when df = 24) = 0.1636<BR>\n" );
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document.write( "e. What is the probability that this sample will be one of the samples that will have a mean SAT Quantitative score between 485 and 525?<BR>\n" );
document.write( "Find the t-scores and find that probability between them_____________________ <BR>\n" );
document.write( "f. Suppose we obtain a mean SAT Quantitative Score of 515. What is the 95% confidence interval for these data?<BR>\n" );
document.write( "x-bar = 515<BR>\n" );
document.write( "ME = 2.06*20 = 41.28<BR>\n" );
document.write( "95% CI: 515-41.28 < u < 515+41.28<BR>\n" );
document.write( "_____________________ \r<BR>\n" );
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document.write( "g. Supposed we obtain a mean SAT Quantitative Score of 487. What is the 80% confidence interval for these data?<BR>\n" );
document.write( "487-ME < u < 487+ME<BR>\n" );
document.write( "ME = 1.32*20 = 26.36<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============\r<BR>\n" );
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