document.write( "Question 1192816: You randomly select 650 home-accident deaths and find that 117 of them are caused by falls. Construct the 99% confidence interval for the true population proportion of all of the home-accident deaths caused by falls.
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Algebra.Com's Answer #824742 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "n = 650 = sample size \n" ); document.write( "x = 117 = number of falls \n" ); document.write( "phat = x/n = 117/650 = 0.18\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "At 99% confidence, we have z = 2.576 as the approximate critical value. \n" ); document.write( "This value is used often in confidence intervals that you should memorize it, or have it handy on a reference table.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "E = margin of error \n" ); document.write( "E = z*sqrt(phat*(1-phat)/n) \n" ); document.write( "E = 2.576*sqrt(0.18*(1-0.18)/650) \n" ); document.write( "E = 0.03881792879981 \n" ); document.write( "E = 0.0388 \n" ); document.write( "which is approximate\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "L = lower boundary \n" ); document.write( "L = phat - E \n" ); document.write( "L = 0.18 - 0.0388 \n" ); document.write( "L = 0.1412\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "U = upper boundary \n" ); document.write( "U = phat + E \n" ); document.write( "U = 0.18 + 0.0388 \n" ); document.write( "U = 0.2188\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Answer: (0.1412, 0.2188) \n" ); document.write( "The boundary values are approximate because the value of E was approximate. Round however instructed.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "An alternative way to express the confidence interval is to write 0.1412 < p < 0.2188 \n" ); document.write( "This shows that we're 99% confident the population proportion (p) is somewhere between 0.1412 and 0.2188 \n" ); document.write( "In other words, we're 99% confident the population percentage is between roughly 14.12% and roughly 21.88% \n" ); document.write( " \n" ); document.write( " |