document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039097>Question 1039097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of 800 registered voters in Flagstaff found 456 registered voters who support immigration reform. Find a 95% confidence interval for the true percent of registered voters in Flagstaff who support immigration reform. Express your results to the nearest hundredth of a percent. .\r<BR>\n" );
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document.write( "Answer: \r<BR>\n" );
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document.write( "____ to____% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653830 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=653830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given information<BR>\n" );
document.write( "x = 456 (number of successes)<BR>\n" );
document.write( "n = 800 (sample size)<BR>\n" );
document.write( "Confidence Level = 95%\r<BR>\n" );
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document.write( "What we want to find: \r<BR>\n" );
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document.write( "We want to find the lower (L) and upper (U) boundaries of the confidence interval\r<BR>\n" );
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document.write( "The critical value of the 95% confidence interval is z = 1.96 (approximately). You can determine this by using a table like <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">this one</a>. Look at the confidence level 95% (bottom of page) then look directly above it to find the value of 1.960 which is the same as 1.96\r<BR>\n" );
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document.write( "Sample proportion <BR>\n" );
document.write( "p = x/n = 456/800 = 0.57\r<BR>\n" );
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document.write( "Standard Error (SE)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+sqrt%28%280.57%2A%281-0.57%29%29%2F800%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%28%280.57%2A%281-0.57%29%29%2F800%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+sqrt%28%280.57%2A%280.43%29%29%2F800%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%28%280.57%2A%280.43%29%29%2F800%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+sqrt%280.2451%2F800%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%280.2451%2F800%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+sqrt%280.000306375%29 ALIGN=MIDDLE  ALT=\"SE+=+sqrt%280.000306375%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE+=+0.01750357106421 ALIGN=MIDDLE  ALT=\"SE+=+0.01750357106421\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Margin of Error (ME)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ME+=+z%2ASE ALIGN=MIDDLE  ALT=\"ME+=+z%2ASE\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ME+=+1.96%2A0.01750357106421 ALIGN=MIDDLE  ALT=\"ME+=+1.96%2A0.01750357106421\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ME+=+0.03430699928586 ALIGN=MIDDLE  ALT=\"ME+=+0.03430699928586\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The lower boundary of the confidence interval is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+p+-+ME ALIGN=MIDDLE  ALT=\"L+=+p+-+ME\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+0.57+-+0.03430699928586 ALIGN=MIDDLE  ALT=\"L+=+0.57+-+0.03430699928586\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+0.53569300071414 ALIGN=MIDDLE  ALT=\"L+=+0.53569300071414\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That turns into 53.569300071414% which rounds to 53.57%\r<BR>\n" );
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document.write( "So L = 53.57% approximately \r<BR>\n" );
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document.write( "The upper boundary of the confidence interval is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+p+%2B+ME ALIGN=MIDDLE  ALT=\"U+=+p+%2B+ME\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+0.57+%2B+0.03430699928586 ALIGN=MIDDLE  ALT=\"U+=+0.57+%2B+0.03430699928586\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+0.60430699928587 ALIGN=MIDDLE  ALT=\"U+=+0.60430699928587\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That turns into 60.430699928587% which rounds to 60.43%\r<BR>\n" );
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document.write( "So U = 60.43% approximately\r<BR>\n" );
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document.write( "To recap, the lower and upper bound (L and U respectively) of the confidence interval is\r<BR>\n" );
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document.write( "L = 53.57%<BR>\n" );
document.write( "U = 60.43% \r<BR>\n" );
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document.write( "where the boundaries are in percentage form\r<BR>\n" );
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document.write( "Final Answer:<BR>\n" );
document.write( "<font color=black><u>&nbsp;&nbsp;&nbsp;<font color=red>53.57</font>&nbsp;&nbsp;&nbsp;</u></font> to <font color=black><u>&nbsp;&nbsp;&nbsp;<font color=red>60.43</font>&nbsp;&nbsp;&nbsp;</u></font>% </SPAN>\n" );
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