document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197542>Question 1197542</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 400 adult residents sampled, 288 had kids. Based on this, construct a 99% 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 < <BR>\n" );
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 = <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830844 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "At 99% confidence, the z critical value is roughly z = 2.576<BR>\n" );
document.write( "Use a table like this<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "to get that value. Look at the bottom row labeled \"Z\" and above the 99% confidence level.\r<BR>\n" );
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document.write( "Alternatively, you can use the NormInv function on a spreadsheet to calculate the z critical value.\r<BR>\n" );
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document.write( "x = 288 = number of people who have children<BR>\n" );
document.write( "n = 400 = sample size<BR>\n" );
document.write( "phat = sample proportion of people who have children<BR>\n" );
document.write( "phat = x/n<BR>\n" );
document.write( "phat = 288/400<BR>\n" );
document.write( "phat = 0.72\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 = 2.576*sqrt(0.72*(1-0.72)/400)<BR>\n" );
document.write( "E = 0.058\r<BR>\n" );
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document.write( "L = lower boundary of the confidence interval<BR>\n" );
document.write( "L = phat - E<BR>\n" );
document.write( "L = 0.72 - 0.058<BR>\n" );
document.write( "L = 0.662\r<BR>\n" );
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document.write( "U = upper boundary of the confidence interval<BR>\n" );
document.write( "U = phat + E<BR>\n" );
document.write( "U = 0.72 + 0.058<BR>\n" );
document.write( "U = 0.778\r<BR>\n" );
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document.write( "The confidence interval in the format L < p < U is <font color=red>0.662 < p < 0.778</font>\r<BR>\n" );
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document.write( "When written in the format phat ± E, we get <font color=red>0.72 ± 0.058</font><BR>\n" );
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