document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194702>Question 1194702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=27.3. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required? \r<BR>\n" );
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document.write( "I keep getting 264 as the answer which it says is incorrect, maybe it is my z-score? </SPAN>\n" );
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document.write( "At 95% confidence, the z critical value is roughly z = 1.960<BR>\n" );
document.write( "Use a Z table or calculator to determine this. \r<BR>\n" );
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document.write( "We're told that sigma = 27.3<BR>\n" );
document.write( "The error we want is E = 2 or smaller.\r<BR>\n" );
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document.write( "Let's compute the min sample size.<BR>\n" );
document.write( "n = (z*sigma/E)^2<BR>\n" );
document.write( "n = (1.960*27.3/2)^2<BR>\n" );
document.write( "n = 715.776516<BR>\n" );
document.write( "n = <font color=red>716</font><BR>\n" );
document.write( "Always round up to the nearest whole number. <BR>\n" );
document.write( "If we got something like 715.00001, then we would still round up to 716 to clear the hurdle.\r<BR>\n" );
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document.write( "Here is a short derivation of where this version of min sample size formula comes from<BR>\n" );
document.write( "E = margin of error<BR>\n" );
document.write( "E = z*sigma/sqrt(n)<BR>\n" );
document.write( "E*sqrt(n) = z*sigma<BR>\n" );
document.write( "sqrt(n) = z*sigma/E<BR>\n" );
document.write( "n = (z*sigma/E)^2\r<BR>\n" );
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document.write( "Answer: <font color=red>716</font><BR>\n" );
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