document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638003>Question 638003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a sample is drawn and z(&#945;/2) = 1.96 and &#963; = 30.  Answer the following questions:<BR>\n" );
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document.write( "(A)    If the Maximum Error of Estimate is 0.04 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 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401964 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=401964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that a sample is drawn and z(&#945;/2) = 1.96 and &#963; = 30. Answer the following questions:\r<BR>\n" );
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document.write( "(A) If the Maximum Error of Estimate is 0.04 for this sample, what would be the sample size?<BR>\n" );
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document.write( "n = [z*s/E]^2<BR>\n" );
document.write( "n = [1.96*30/0.04]^2 = 2,160,900\r<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" );
document.write( "400 = [1.96*30/E]^2<BR>\n" );
document.write( "1.96*30/E = 20<BR>\n" );
document.write( "E = 1.96*30/20<BR>\n" );
document.write( "E = 2.94<BR>\n" );
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document.write( "(C) What happens to the Maximum Error of Estimate as the sample size gets smaller?<BR>\n" );
document.write( "n = [z*s/E]^2<BR>\n" );
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document.write( "Notice that n and E are inversely related.<BR>\n" );
document.write( "So, as n gets smaller, E get 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?<BR>\n" );
document.write( "The width of the confidence interval is ALWAYS twice as large as the max. error.<BR>\n" );
document.write( "So, as the sample size gets smaller, the CI gets wider.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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