document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110326>Question 1110326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher wishes to&#8203; estimate, with <BR>\n" );
document.write( "9999&#8203;% <BR>\n" );
document.write( "&#8203;confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within <BR>\n" );
document.write( "44&#8203;% <BR>\n" );
document.write( "of the true proportion.<BR>\n" );
document.write( "&#8203;a) No preliminary estimate is available. Find the minimum sample size needed.\r<BR>\n" );
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document.write( "&#8203;b) Find the minimum sample size&#8203; needed, using a prior study that found that <BR>\n" );
document.write( "1818&#8203;% <BR>\n" );
document.write( "of the  respondents said they think their president can control the price of gasoline.<BR>\n" );
document.write( "&#8203;c) Compare the results from parts&#8203; (a) and&#8203; (b).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725727 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Within 4% and confidence 99%<BR>\n" );
document.write( "the error 0.04=z* sqrt (SE), where z=2.576 and SE is sqrt (p*(1-p))/n.  Use 0.5 when no estimate is available, since that is the most conservative (largest) product of two decimals whose sum is 1.<BR>\n" );
document.write( "2.576*sqrt(0.25)/sqrt (n) equals error<BR>\n" );
document.write( "2.576*0.5/sqrt (n)=0.04<BR>\n" );
document.write( "1.288/0.04=sqrt(n); square both sides<BR>\n" );
document.write( "n=1036.84 or 1037.\r<BR>\n" );
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document.write( "With a known fraction of 0.18, p*(1-p)=0.1476<BR>\n" );
document.write( "(1.288/0.1476)^2=76.15 or 77<BR>\n" );
document.write( "When a prior estimate is available and is significantly different from 0.5, the sample size falls dramatically.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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