document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174399>Question 1174399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Dean of a college wants to use the proportion of a population to determine the sample size needed to interview regarding their thoughts about the new school structures.She want to be able to assert with a probability 0.95 that her error will be at most 0.05. Similar pols in the past showed that 65% approved the new structure. How large a sample does the Dean need?<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 #850669 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.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=850669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Identify the Parameters:**\r<BR>\n" );
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document.write( "* Confidence Level: 95%  (This gives us a z-score of 1.96)<BR>\n" );
document.write( "* Margin of Error (E): 0.05<BR>\n" );
document.write( "* Estimated Population Proportion (p̂): 0.65 (from past polls)<BR>\n" );
document.write( "* Estimated Population Proportion who don't approve (q̂) = 1 - p̂ = 0.35\r<BR>\n" );
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document.write( "**2. Use the Sample Size Formula:**\r<BR>\n" );
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document.write( "The formula for calculating the sample size (n) for estimating a population proportion is:\r<BR>\n" );
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document.write( "n = (z^2 * p̂ * q̂) / E^2\r<BR>\n" );
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document.write( "**3. Plug in the Values:**\r<BR>\n" );
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document.write( "n = (1.96^2 * 0.65 * 0.35) / 0.05^2\r<BR>\n" );
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document.write( "**4. Calculate:**\r<BR>\n" );
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document.write( "n ≈ 350.28\r<BR>\n" );
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document.write( "**5. Round Up:**\r<BR>\n" );
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document.write( "Since we cannot have a fraction of a person, always round the sample size up to the nearest whole number.\r<BR>\n" );
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document.write( "n = 351\r<BR>\n" );
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document.write( "**Therefore, the Dean needs a sample size of 351 students to achieve the desired level of confidence and margin of error.** </SPAN>\n" );
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