document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137046>Question 137046</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534387772/algebrahomeworkh>A Brief Introduction to Probability and Statistics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of n=64 observations has a mean x(bar)=29.1 and a standard deviation s=3.9.\r<BR>\n" );
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document.write( "a) Give the point estimate of the population mean mu and find the margin of error for your estimate.\r<BR>\n" );
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document.write( "b) Find a 90% confidence interval for mu. what does \"90% confident\" mean?\r<BR>\n" );
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document.write( "c) Find a 90% lower confidence bound for the population mean mu. Why is this bound different from the lower confidence limit in part b?\r<BR>\n" );
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document.write( "d) How many observations do you need to estimate mu to within .5, with probability equal to .95? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100285 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=100285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A random sample of n=64 observations has a mean x(bar)=29.1 and a standard deviation s=3.9. <BR>\n" );
document.write( "a) Give the point estimate of the population mean mu and find the margin of error for your estimate.<BR>\n" );
document.write( "point estimate: 29.1<BR>\n" );
document.write( "margin of error: s/sqrt(n) = 3.9/sqrt(64) = 0.4875<BR>\n" );
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document.write( "b) Find a 90% confidence interval for mu. what does \"90% confident\" mean?<BR>\n" );
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document.write( "Comment: I am using z=1.645 for 90% CI<BR>\n" );
document.write( "29.1-1.45*0.4875 < mu < 20.1+0.4875<BR>\n" );
document.write( "90% confident means just that; It does not mean there is a 90% probability.<BR>\n" );
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document.write( "c) Find a 90% lower confidence bound for the population mean mu. Why is this bound different from the lower confidence limit in part b?<BR>\n" );
document.write( "???<BR>\n" );
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document.write( "d) How many observations do you need to estimate mu to within .5, with probability equal to .95?<BR>\n" );
document.write( "n = [z*s/E]^2<BR>\n" );
document.write( "n = [1.645*3.9/0.5]^2 = 164.634; rounding up, n = 165<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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