document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204908>Question 1204908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a recent survey of 1124 students, 980 of them would like to recommend www.helpyourmath.com to their friends. Construct a 90% confidence interval to estimate the proportion of all students who would recommend www.helpyourmath.com to their friends.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841449 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=841449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean proportion is p = 980/1124 = .871886121.<BR>\n" );
document.write( "q = 1-p = .128113879.<BR>\n" );
document.write( "the standard error is sqrt(p * q / 1124) = sqrt(.871886121*.12811387/1124) = .0099688444.\r<BR>\n" );
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document.write( "the two tailed 90% confidence interval requires a z-score of plus or minus 1.645.\r<BR>\n" );
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document.write( "the z-score formula used is z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the desired proportion.<BR>\n" );
document.write( "m is the mean proportion.<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "to find the lower desired proportion, the formula becomes:<BR>\n" );
document.write( "-1.645 = (x - .871886121) / .009968844.<BR>\n" );
document.write( "solve for x to get x = -1.645 * .009968844 + .871886121 = .855487372.\r<BR>\n" );
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document.write( "to find the upper desired proportion, the formula becomes:<BR>\n" );
document.write( "1.645 = (x - .871886121) / .009968844.<BR>\n" );
document.write( "solve for x to get x = 1.645 * .009968844 + .i71886121 = .88828487.\r<BR>\n" );
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document.write( "round to 3 decimal places to get 90% confidence interval is from .855 to .888.\r<BR>\n" );
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document.write( "since the value is n * p, you get:\r<BR>\n" );
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document.write( "mean is 1124 * 980 / 1124 = 980<BR>\n" );
document.write( "low threshold is 1124 * .855 = 961 roughly.<BR>\n" );
document.write( "high threshold is 1124 * .888 = 998 roughly.\r<BR>\n" );
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document.write( "your solution should be that the 90% confidence interval of the proportion is .855487372 to.88828487.<BR>\n" );
document.write( "round your numbers as required.<BR>\n" );
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