document.write( "Question 1158347: in conducting a hypothetical survey of 650 Kansas city residents, are a researcher found that 45% are fans of the Kansas city Jayhawks\r
\n" ); document.write( "\n" ); document.write( "A. Calculate the margin of error with 95% confidence level survey.\r
\n" ); document.write( "\n" ); document.write( "B. If the researcher wanted to get a margin of error of 2.5 how many additional Kansas city residents would need to survey? Assume the number of residents who are fans of the Kansas Jayhawks stays at 45% \n" ); document.write( "
Algebra.Com's Answer #781282 by Boreal(15235)\"\" \"About 
You can put this solution on YOUR website!
95% CI half-interval for a one sample proportion test is z(0.975)*sqrt(p*(1-p)/n)
\n" ); document.write( "=1.96*sqrt(0.45*0.55/650); sqrt term=0.0195
\n" ); document.write( "=0.038 is half-interval, and this is the margin of error ANSWER
\n" ); document.write( "CI is (0.412, 0.488), adding and subtracting the error to and from the mean\r
\n" ); document.write( "\n" ); document.write( "for an error of 0.025 (presumed that is what is being asked for
\n" ); document.write( "1.96*sqrt(.45*.55/n)=0.025
\n" ); document.write( "1.96*sqrt(0.45*0.55)/0.025=sqrt(n)=39.00
\n" ); document.write( "n=1521.27 round to 1522\r
\n" ); document.write( "\n" ); document.write( "by rounding earlier, the sample size will be 1521.
\n" ); document.write( "There is slight error in the CI in that 45% of 650 is not an integer, so mathematically the CI can be done but on a calculator an integer must be used, so the exact percentage won't be 45%\r
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