document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136446>Question 136446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds. <BR>\n" );
document.write( "a. What is the value of the population mean? What is the best estimate of this value? <BR>\n" );
document.write( "b. Explain why we need to use the t distribution. What assumption do you need to make? <BR>\n" );
document.write( "c. For a 90% confidence interval, what is the value of t? <BR>\n" );
document.write( "d. Develop the 90% confidence interval for the population mean. <BR>\n" );
document.write( "e. Would it be reasonable to conclude that the population mean is 63 pounds? <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 #99950 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=99950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds. <BR>\n" );
document.write( "a. What is the value of the population mean? 60 lbs<BR>\n" );
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document.write( "What is the best estimate of this value? The mean of the same is your best est.<BR>\n" );
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document.write( "b. Explain why we need to use the t distribution.<BR>\n" );
document.write( "You are estimating the population mean.<BR>\n" );
document.write( "Comment: Every text differs on the reasoning for this. Check your text.<BR>\n" );
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document.write( "What assumption do you need to make?<BR>\n" );
document.write( "The amount of sugar consumed by people is normally distributed.<BR>\n" );
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document.write( "c. For a 90% confidence interval, what is the value of t? <BR>\n" );
document.write( "That depends on the degrees of freedom for the problem.<BR>\n" );
document.write( "In your problem df=15, so the t-value is 1.753<BR>\n" );
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document.write( "d. Develop the 90% confidence interval for the population mean.<BR>\n" );
document.write( "x-bar = 60<BR>\n" );
document.write( "E = 1.753 = 8.765<BR>\n" );
document.write( " 90% CI: (60-8.765 < u < 60+8.765) = 51.235 < u < 68.765<BR>\n" );
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document.write( "e. Would it be reasonable to conclude that the population mean is 63 pounds? <BR>\n" );
document.write( "At this point all you could say is that the value is in the 90% CI.<BR>\n" );
document.write( "You cannot claim that you have 90% confidence that the mean is 63 lbs.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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