document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=633821>Question 633821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 180 was taken, and the mean amount spent was $219.76. Assuming a standard deviation equal to $41.77, find the 99% confidence interval for m, the mean for all such families (show all work). \r<BR>\n" );
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document.write( "2.  Assume that a sample is drawn and z(&#945;/2) = 1.65 and &#963; = 15.  Answer the following questions:<BR>\n" );
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document.write( "(A)If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?<BR>\n" );
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document.write( "(B)Given that the sample Size is 400 with this same z(&#945;/2) and &#963;, what would be the Maximum Error of Estimate?<BR>\n" );
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document.write( "(C)   What happens to the Maximum Error of Estimate as the sample size gets larger?<BR>\n" );
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document.write( "(D)   What effect does the answer to C above have to the size of the confidence interval? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399180 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=399180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 180 was taken, and the mean amount spent was $219.76. Assuming a standard deviation equal to $41.77, find the 99% confidence interval for m, the mean for all such families (show all work).<BR>\n" );
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document.write( "x-bar = 219.76<BR>\n" );
document.write( "E = 1.645*(41.77/sqrt(180)) = 5.1215<BR>\n" );
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document.write( "90% CI: 219.76-5.12 < x < 219.76+5.12<BR>\n" );
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document.write( "2. Assume that a sample is drawn and z(&#945;/2) = 1.65 and &#963; = 15. Answer the following questions:\r<BR>\n" );
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document.write( "(A)If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size?<BR>\n" );
document.write( "E = z*s/sqrt(n)<BR>\n" );
document.write( "0.05 = 1.65*15/sqrt(n)<BR>\n" );
document.write( "sqrt(n) = 1.65*15/0.05<BR>\n" );
document.write( "sqrt(n) = 495<BR>\n" );
document.write( "n = 22.25 = 22 when rounded down<BR>\n" );
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document.write( "(B)Given that the sample Size is 400 with this same z(&#945;/2) and &#963;, what would be<BR>\n" );
document.write( "the Maximum Error of Estimate?<BR>\n" );
document.write( "Substitute for \"n\" and \"z\" and sigma.<BR>\n" );
document.write( "Then solve for \"E\".<BR>\n" );
document.write( "E = 1.2375<BR>\n" );
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document.write( "(C) What happens to the Maximum Error of Estimate as the sample size gets larger?<BR>\n" );
document.write( "E and sqrt(n) are indirectly related.<BR>\n" );
document.write( "AS n get larger, E get smaller.<BR>\n" );
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document.write( "(D) What effect does the answer to C above have to the size of the confidence interval?<BR>\n" );
document.write( "The size of the CI is ALWAYS 2*E.<BR>\n" );
document.write( "If n get larger, E get smaller, and the CI gets smaller (narrower).<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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