document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=612660>Question 612660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> assume that a sample is drawn and z(a/2)= 1.96 AND 0=25. Answer the following questions:<BR>\n" );
document.write( "a) if the maximum error of estimate is 0.04 for this sample, what would be the sample size?<BR>\n" );
document.write( "b) given that the sample size is 400 with this same z(a/2) and 0, what would be the Maixmum Error of estimate?<BR>\n" );
document.write( "c) what happens to the maximum error of estimate as the sample size gets smaller?<BR>\n" );
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 #385643 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=385643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  assume that a sample is drawn and z(a/2)= 1.96 AND 0=25. Answer the following questions:<BR>\n" );
document.write( "a) if the maximum error of estimate is 0.04 for this sample, what would be the sample size?<BR>\n" );
document.write( "------<BR>\n" );
document.write( "ME = z*s/sqrt(n)<BR>\n" );
document.write( "0.04 = 1.96*25/sqrt(n)<BR>\n" );
document.write( "sqrt(n) = 1.96*25/0.04 = <BR>\n" );
document.write( "n = 35<BR>\n" );
document.write( "====================================<BR>\n" );
document.write( "b) given that the sample size is 400 with this same z(a/2) and s, what would be the Maxmum Error of estimate?<BR>\n" );
document.write( "ME = 1.96*25/sqrt(400) = 2.45<BR>\n" );
document.write( "====================================<BR>\n" );
document.write( "c) what happens to the maximum error of estimate as the sample size gets smaller?<BR>\n" );
document.write( "ME = z*s/sqrt(n)<BR>\n" );
document.write( "Notice that ME and n are inversely related.<BR>\n" );
document.write( "As n gets smaller, ME gets larger.<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
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*ME<BR>\n" );
document.write( "So, as n gets smaller, ME get larger, and CI get larger.<BR>\n" );
document.write( "That means, as the sample size gets smaller the CI has to<BR>\n" );
document.write( "be broader so we can have the same level of confidence that<BR>\n" );
document.write( "it contains the population parameter we are interested in.<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );