document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089638>Question 1089638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After calculating the sample size needed to estimate a population proportion to within .04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led t a sample size of 800, the sample size will now have to be:\r<BR>\n" );
document.write( "\n" );
document.write( "I know the answer but do not know how to get it. Can someone please help me?! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703987 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=703987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "We will use the formula <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+p%281-p%29%28z%2FE%29%5E2 ALIGN=MIDDLE  ALT=\"n+=+p%281-p%29%28z%2FE%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "as shown on <a  rel=nofollow HREF=\"https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm\">this page</a> (scroll down to the section titled \"Finding n to Estimate a Proportion\")\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Initially we're told that an error of E = 0.04 will lead to a sample size of n = 800. We don't know z and we don't know p. We don't need to know p. If p is unknown, then we assume that p = 0.5. The goal here is to find z given n = 800 and E = 0.04. Let's do that\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+p%281-p%29%28z%2FE%29%5E2 ALIGN=MIDDLE  ALT=\"n+=+p%281-p%29%28z%2FE%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800+=+0.5%281-0.5%29%28z%2F0.04%29%5E2 ALIGN=MIDDLE  ALT=\"800+=+0.5%281-0.5%29%28z%2F0.04%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800+=+0.25%28z%2F0.04%29%5E2 ALIGN=MIDDLE  ALT=\"800+=+0.25%28z%2F0.04%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800%2F0.25+=+%28z%2F0.04%29%5E2 ALIGN=MIDDLE  ALT=\"800%2F0.25+=+%28z%2F0.04%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3200+=+%28z%2F0.04%29%5E2 ALIGN=MIDDLE  ALT=\"3200+=+%28z%2F0.04%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2F0.04%29%5E2+=+3200 ALIGN=MIDDLE  ALT=\"%28z%2F0.04%29%5E2+=+3200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F0.04+=+sqrt%283200%29 ALIGN=MIDDLE  ALT=\"z%2F0.04+=+sqrt%283200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F0.04+=+56.5685424949239 ALIGN=MIDDLE  ALT=\"z%2F0.04+=+56.5685424949239\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+0.04%2A56.5685424949239 ALIGN=MIDDLE  ALT=\"z+=+0.04%2A56.5685424949239\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+2.26274169979696 ALIGN=MIDDLE  ALT=\"z+=+2.26274169979696\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the z critical value is roughly z = 2.2627\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll use z = 2.2627 and the new error threshold of E = 0.01 to find n to be...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+p%281-p%29%28z%2FE%29%5E2 ALIGN=MIDDLE  ALT=\"n+=+p%281-p%29%28z%2FE%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+0.5%281-0.5%29%282.2627%2F0.01%29%5E2 ALIGN=MIDDLE  ALT=\"n+=+0.5%281-0.5%29%282.2627%2F0.01%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+0.25%28226.27%29%5E2 ALIGN=MIDDLE  ALT=\"n+=+0.25%28226.27%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+0.25%2A51198.1129 ALIGN=MIDDLE  ALT=\"n+=+0.25%2A51198.1129\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+12799.528225 ALIGN=MIDDLE  ALT=\"n+=+12799.528225\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+12800 ALIGN=MIDDLE  ALT=\"n+=+12800\"   DISABLED_style= \"max-width:90%; height:auto;\" > (round up to the nearest whole number)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The new sample size needed is approximately 12800 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "</font>  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );