document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193142>Question 1193142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the minimum sample size n needed to estimate sigma for the given values of c, sigma ,and E. c = 0.98; sigma = 6.9 and E = 2 Assume that a preliminary sample has at least 30 members . n =___ ( Round up to the nearest whole number). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848943 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=848943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the z-score for the given confidence level (c = 0.98)**\r<BR>\n" );
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document.write( "* Since c = 0.98, the alpha level (α) is 1 - 0.98 = 0.02.<BR>\n" );
document.write( "* We need to find the z-score that corresponds to an area of 1 - α/2 = 0.99 in the standard normal distribution table.<BR>\n" );
document.write( "* The z-score for 0.99 is approximately 2.33.\r<BR>\n" );
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document.write( "**2. Use the formula for sample size (n)**\r<BR>\n" );
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document.write( "* The formula to determine the minimum sample size (n) needed to estimate the population standard deviation (σ) with a given confidence level and margin of error (E) 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:<BR>\n" );
document.write( "      * n is the sample size<BR>\n" );
document.write( "      * z is the z-score corresponding to the desired confidence level<BR>\n" );
document.write( "      * σ is the population standard deviation<BR>\n" );
document.write( "      * E is the desired margin of error\r<BR>\n" );
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document.write( "* Substitute the given values:\r<BR>\n" );
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document.write( "   n = (2.33 * 6.9 / 2)² <BR>\n" );
document.write( "   n = (16.077 / 2)² <BR>\n" );
document.write( "   n = 8.0385² <BR>\n" );
document.write( "   n ≈ 64.62\r<BR>\n" );
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document.write( "**3. Round up to the nearest whole number**\r<BR>\n" );
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document.write( "* Since we need a whole number of samples, round up n to 65.\r<BR>\n" );
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document.write( "**Therefore, the minimum sample size (n) needed to estimate sigma for the given values is 65.**<BR>\n" );
document.write( " </SPAN>\n" );
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