document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191680>Question 1191680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 3 units?\r<BR>\n" );
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document.write( "28      21        37        38        24        28        38        47        27        32        36        43\r<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 #849148 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the required sample size:\r<BR>\n" );
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document.write( "**1. Identify the Key Values:**\r<BR>\n" );
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document.write( "* **Margin of Error (E):** 3 units<BR>\n" );
document.write( "* **Confidence Level:** 95%  This corresponds to a Z-score of 1.96.<BR>\n" );
document.write( "* **Population Standard Deviation (σ):**  Since we don't know the population standard deviation, we'll use the sample standard deviation as an estimate.\r<BR>\n" );
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document.write( "**2. Calculate the Sample Standard Deviation:**\r<BR>\n" );
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document.write( "First, calculate the mean of the given BMI values:\r<BR>\n" );
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document.write( "Mean = (28 + 21 + 37 + 38 + 24 + 28 + 38 + 47 + 27 + 32 + 36 + 43) / 12 = 32.58\r<BR>\n" );
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document.write( "Next, calculate the squared difference between each value and the mean, sum these squared differences, and divide by (n-1) to get the variance. Then take the square root to get the standard deviation.\r<BR>\n" );
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document.write( "Standard Deviation (s) ≈ 7.14 (You can use a calculator or spreadsheet software for this).\r<BR>\n" );
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document.write( "**3. Use the Sample Size Formula:**\r<BR>\n" );
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document.write( "The formula for calculating the sample size (n) is:\r<BR>\n" );
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document.write( "n = (Z * σ / E)²\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* n = sample size<BR>\n" );
document.write( "* Z = Z-score<BR>\n" );
document.write( "* σ = population standard deviation (estimated by the sample standard deviation)<BR>\n" );
document.write( "* E = margin of error\r<BR>\n" );
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document.write( "**4. Plug in the Values and Calculate:**\r<BR>\n" );
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document.write( "n = (1.96 * 7.14 / 3)²<BR>\n" );
document.write( "n = (4.65)²<BR>\n" );
document.write( "n ≈ 21.62\r<BR>\n" );
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document.write( "**5. Round Up:**\r<BR>\n" );
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document.write( "Since you can't have a fraction of a subject, always round the sample size up to the nearest whole number.  Therefore, you would need 22 subjects.<BR>\n" );
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