document.write( "Question 276876: Statistics word problem:\r
\n" ); document.write( "\n" ); document.write( "We are interested in estimating how many New Jersey residents support moving the New Jersey presidential primary elections up to early February. We were able to draw a simple random sample that includes 400 New Jersey residents. Sixty-five percent of respondents supported the change, with as standard deviation of 40. We can be 95% confident that the actual mean in the New Jersey population lies between the ___% and ___%. We can be 99% confident that the actual mean in the population lies between ___% and ___%.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #201717 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
We are interested in estimating how many New Jersey residents support moving the New Jersey presidential primary elections up to early February. We were able to draw a simple random sample that includes 400 New Jersey residents. Sixty-five percent of respondents supported the change, with a standard deviation of 40.\r
\n" ); document.write( "\n" ); document.write( " We can be 95% confident that the actual mean in the New Jersey population lies between the ___% and ___%.
\n" ); document.write( "---
\n" ); document.write( "sample p-hat = 0.65
\n" ); document.write( "standard error = E = 1.96*sqrt[0.65*0.35/400] = 0.0467
\n" ); document.write( "95% CI: 0.65-0.0467 < p < 0.65+0.0467
\n" ); document.write( "95% CI: 0.6033 < p < 0.6967
\n" ); document.write( "==========================================================\r
\n" ); document.write( "\n" ); document.write( "We can be 99% confident that the actual mean in the population lies between
\n" ); document.write( "sample mean = 0.65*400 = 260
\n" ); document.write( "standard error = E = invT(0.995,399)*40/sqrt(400) = 2.588*2 = 5.1764
\n" ); document.write( "99% CI; 260-5.1764 < u < 260+5.1764
\n" ); document.write( "99% CI: 254.82 < u < 265.18
\n" ); document.write( "==================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " ___% and ___%.
\n" ); document.write( " \n" ); document.write( "
\n" );