document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207432>Question 1207432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kara surveyed 200 people, chosen at random on thompson drive, to try to determine what % of thompsonites are skiers. 86 people in her sample said they were skiers. \r<BR>\n" );
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document.write( "A.) What is the 95% confidence interval for the percent of Thompsonites who are skiers ? (Formula: 95% confidence interval = mean ± 1.96(standard deviation)<BR>\n" );
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document.write( "B.) Calculate the margin of error.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845300 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=845300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 200<BR>\n" );
document.write( "p = 86/200 = .43.<BR>\n" );
document.write( "q = (1 - 86/200) = 114/200 = .57.<BR>\n" );
document.write( "s = sqrt(.43 * .57 / 200) = .035007 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "critical z-score at 95% confidence interval is z = plus or minus 1.96.\r<BR>\n" );
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document.write( "z-score formula is z = (x-m)/s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the critical raw score.<BR>\n" );
document.write( "m is the raw mean which is equal to p.<BR>\n" );
document.write( "s is the standard error which is equal to s.\r<BR>\n" );
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document.write( "on the high side of the confidence interval, the formula becomes 1.96 = (x - .43) / .035007.<BR>\n" );
document.write( "solve for x to get x = 1.96 * .035007 + .43 = .49861372.\r<BR>\n" );
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document.write( "on the low side of the confidence interval, the formula becomes -1.906 = (x - .43) / .035007.<BR>\n" );
document.write( "solve for x to get x = -1.96 * .035007 + .43 = .36138628.\r<BR>\n" );
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document.write( "the 95% confidence interval is .36138628 to .49861372.\r<BR>\n" );
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document.write( "the margin of error is (.49861372 minus .36138628) / 2 = .06861375.\r<BR>\n" );
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