document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086255>Question 1086255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 99% confidence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700552 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=700552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> interval is 0.03<BR>\n" );
document.write( "2.576*SE is 99% confidence<BR>\n" );
document.write( "SE is sqrt (0.4)(0.6) or p(1-p)/n<BR>\n" );
document.write( "Therefore,<BR>\n" );
document.write( "0.03=2.576* sqrt (0.24/n)<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "0.0009=6.64*0.24/n<BR>\n" );
document.write( "0.0009n=1.59.  I haven't rounded, but dividing now by 0.0009 gives n=1769.54, or 1770. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );