document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202947>Question 1202947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 325 had kids. Based on this, construct a 95% confidence interval for the proportion p of adult residents who are parents in this county.\r<BR>\n" );
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document.write( "Express your answer in tri-inequality form. Give your answers as decimals, to three places.\r<BR>\n" );
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document.write( "______< p < _____ \r<BR>\n" );
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document.write( "Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.\r<BR>\n" );
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document.write( "p = (.65) |plus or minus| __________ </SPAN>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red>0.608</font> < p < <font color=red>0.692</font>\r<BR>\n" );
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document.write( "p = 0.65 plusMinus <font color=red>0.042</font> \r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "phat = 325/500 = 0.65 = sample proportion<BR>\n" );
document.write( "n = 500 = sample size\r<BR>\n" );
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document.write( "z = 1.960 at 95% confidence\r<BR>\n" );
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document.write( "E = margin of error<BR>\n" );
document.write( "E = z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "E = 1.960*sqrt(0.65*(1-0.65)/500)<BR>\n" );
document.write( "E = 0.0418082288551<BR>\n" );
document.write( "E = 0.042\r<BR>\n" );
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document.write( "L = lower boundary<BR>\n" );
document.write( "L = phat - E<BR>\n" );
document.write( "L = 0.65 - 0.042<BR>\n" );
document.write( "L = 0.608\r<BR>\n" );
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document.write( "U = upper boundary<BR>\n" );
document.write( "U = phat + E<BR>\n" );
document.write( "U = 0.65 + 0.042<BR>\n" );
document.write( "U = 0.692\r<BR>\n" );
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document.write( "The 95% confidence interval for p is roughly <font color=red>0.608</font> < p < <font color=red>0.692</font><BR>\n" );
document.write( "We can optionally condense that to the notation (0.608, 0.692); however, your teacher is opting for the more descriptive notation.\r<BR>\n" );
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document.write( "Yet another type of confidence interval notation would be to write p = 0.65 plusMinus <font color=red>0.042</font> where the 0.042 refers to the approximate margin of error.<BR>\n" );
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