document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181457>Question 1181457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be: *<BR>\n" );
document.write( "2 points<BR>\n" );
document.write( "4000.<BR>\n" );
document.write( "1600.<BR>\n" );
document.write( "800.<BR>\n" );
document.write( "200. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813727 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard error for population sample proportion is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5Be%5D+=+sqrt%28%28p%281-p%29%29%2Fn%29 ALIGN=MIDDLE  ALT=\"s%5Be%5D+=+sqrt%28%28p%281-p%29%29%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It is initially known that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28p%281-p%29%29%2F400%29+=+0.05 ALIGN=MIDDLE  ALT=\"sqrt%28%28p%281-p%29%29%2F400%29+=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%281-p%29%29%2F400+=+0.05%5E2+=+1%2F400 ALIGN=MIDDLE  ALT=\"%28p%281-p%29%29%2F400+=+0.05%5E2+=+1%2F400\"   DISABLED_style= \"max-width:90%; height:auto;\" > ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281-p%29+=+1 ALIGN=MIDDLE  ALT=\"p%281-p%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Then from the new requirement of a standard error of 0.025, \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28p%281-p%29%29%2Fn%29+=+sqrt%281%2Fn%29+=+0.025 ALIGN=MIDDLE  ALT=\"sqrt%28%28p%281-p%29%29%2Fn%29+=+sqrt%281%2Fn%29+=+0.025\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fn+=+0.025%5E2+=+1%2F1600 ALIGN=MIDDLE  ALT=\"1%2Fn+=+0.025%5E2+=+1%2F1600\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after squaring both sides.\r<BR>\n" );
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document.write( "From this we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n+=+1600%29 ALIGN=MIDDLE  ALT=\"highlight%28n+=+1600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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