document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149653>Question 1149653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During a period of 11​ years, of 1800 that were selected for grand jury​ duty, 25% of them were immigrants. Construct a 99% confidence interval for the percentage of grand jury members who were immigrants.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770989 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=770989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "Given information<BR>\n" );
document.write( "The value \"11 years\" is not used at all. <BR>\n" );
document.write( "phat = 0.25 is the sample proportion<BR>\n" );
document.write( "n = 1800 is the sample size\r<BR>\n" );
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document.write( "At 99% confidence, the critical z value is approximately z = 2.576<BR>\n" );
document.write( "I used <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">this table</a> to find the critical z value. A similar table should be found in the appendix section of your textbook. <BR>\n" );
document.write( "If you choose to use the table I have linked, then locate the bottom row that shows \"99% confidence level\". Afterward look just above that to find 2.576<BR>\n" );
document.write( "Alternatively you can use the invNorm function on your TI83 or TI84 calculator to get the same approximate value.\r<BR>\n" );
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document.write( "Lets compute the lower bound (L) and the upper bound (U) of the confidence interval. \r<BR>\n" );
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document.write( "L = lower bound of confidence interval<BR>\n" );
document.write( "L = phat - z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "L = 0.25 - 2.576*sqrt(0.25*(1-0.25)/1800)<BR>\n" );
document.write( "L = 0.22370881009412<BR>\n" );
document.write( "L = 0.22\r<BR>\n" );
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document.write( "U = upper bound of confidence interval<BR>\n" );
document.write( "U = phat + z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "U = 0.25 + 2.576*sqrt(0.25*(1-0.25)/1800)<BR>\n" );
document.write( "U = 0.27629118990588<BR>\n" );
document.write( "U = 0.28\r<BR>\n" );
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document.write( "The 99% confidence interval is <font color=red size=4>(0.22, 0.28)</font><BR>\n" );
document.write( "This means at 99% confidence we can say 0.22 < p < 0.28, where p is the population proportion of immigrants selected for grand jury duty. <BR>\n" );
document.write( "This is over the time span of the 11 years mentioned. <BR>\n" );
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