document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187550>Question 1187550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Out of 300 people sampled, 177 preferred Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A.\r<BR>\n" );
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document.write( "Use a 90% confidence level, and give your answers as decimals, to three places.\r<BR>\n" );
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document.write( "_______ < P > ________ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819203 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = 177 / 300 = .59<BR>\n" );
document.write( "q = 1 - p = .41\r<BR>\n" );
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document.write( "mean proportion = p = .59\r<BR>\n" );
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document.write( "standard error = sqrt(p * (1-p / 300) = sqrt(.59 * .41 / 300) = .028396.\r<BR>\n" );
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document.write( "critical z-score at 90% confidence level is plus or minus 1.645.\r<BR>\n" );
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document.write( "use the z-score formula to find the critical raw score.\r<BR>\n" );
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document.write( "for the low side, z = (x - m) / s becomes:\r<BR>\n" );
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document.write( "-1.645 = (x - .59) / .028396.\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = -1.645 * .0283960091 + .59 = .54329.\r<BR>\n" );
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document.write( "for the high side, z = (x - m) / s becomes:\r<BR>\n" );
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document.write( "1.645 = (x - .59) / .028396.\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 1.645 * .028396. + .59 = .63671.\r<BR>\n" );
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document.write( "at 90% confidence level, your proportion will be between .54329 and .63671, when you have a mean of .59 and a standard error of .028396.\r<BR>\n" );
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document.write( "here's what it looks like on a z-score normal distribution calculator output.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/112506.jpg\" >\r<BR>\n" );
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document.write( "the calculator i used can be found at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a> </SPAN>\n" );
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