document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930088>Question 930088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this one? THANK YOU! \r<BR>\n" );
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document.write( "The estimate of the population proportion is to be within plus or minus .02, with a 90 percent level of confidence. The best estimate of the population proportion is .16. How large a sample is required? (Round up your answer to the next whole number.)<BR>\n" );
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document.write( "  Sample size    <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #564697 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=564697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We use the formula n = p(1-p)(z/E)^2 where\r<BR>\n" );
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document.write( "n = min sample size<BR>\n" );
document.write( "p = sample proportion<BR>\n" );
document.write( "z = critical number from the standard normal distribution<BR>\n" );
document.write( "E = margin of error\r<BR>\n" );
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document.write( "In this case,\r<BR>\n" );
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document.write( "p = 0.16  (sample proportion)<BR>\n" );
document.write( "z = 1.64485362695147  (based on the 90% confidence interval)<BR>\n" );
document.write( "E = 0.02 (Margin of error)\r<BR>\n" );
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document.write( "Note: I used a calculator to compute z. You can use a table to find z.\r<BR>\n" );
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document.write( "Let's plug those values into the formula and solve for n\r<BR>\n" );
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document.write( "n = p(1-p)(z/E)^2\r<BR>\n" );
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document.write( "n = 0.16(1-0.16)(1.64485362695147/0.02)^2\r<BR>\n" );
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document.write( "n = 909.062600576059 ... use a calculator here\r<BR>\n" );
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document.write( "n = 910 ... Always round UP (to the nearest whole number)\r<BR>\n" );
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document.write( "Why do we round up? If we rounded down, then we would come up short and the margin of error would be too big. If we used n = 909, then the margin of error would exceed E = 0.02. If we use n = 910, then E would be less than 0.02 as desired.\r<BR>\n" );
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document.write( "So the min sample size required is <font size=5 color=\"red\">910</font>\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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