document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206695>Question 1206695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HighTech Inc. randomly tests its employees about company policies. Last year in the 390 random tests conducted, 12 employees failed the test.\r<BR>\n" );
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document.write( "Develop a 95% confidence interval for the proportion of applicants that fail the test. (Round to three decimal places.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844292 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=844292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> test size = 390<BR>\n" );
document.write( "12 out of 390 failed the test<BR>\n" );
document.write( "failure proportion = 12/390\r<BR>\n" );
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document.write( "p = 12/390<BR>\n" );
document.write( "q = 1 - p = 378/390\r<BR>\n" );
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document.write( "standard error of a proportion = sqrt(p*q/n) = sqrt(12/390 * 378/390 / 390) = .0087445932.\r<BR>\n" );
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document.write( "95% two tail confidence interval required a critical z-score of plus or minus 1.959963986.\r<BR>\n" );
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document.write( "on the low side of the confidence interval, the z-score formula of z = (x - m) / s becomes -1.959963986 = (x - 12/390) / .0087445932.<BR>\n" );
document.write( "solve for x to get x = .013630143.\r<BR>\n" );
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document.write( "on the high side of the confidence interval, the z-score formula of z = (x - m) / s becomes 1.959963986 = (x - 12/390) / .0087445932.<BR>\n" );
document.write( "solve for x to get x = .0479083186.\r<BR>\n" );
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document.write( "that should be your 95% confidence interval.<BR>\n" );
document.write( "i used the calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "here's what it looks like using that calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/032705.jpg\">\r<BR>\n" );
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document.write( "the calculator truncates inputs to 6 or 7 decimal digits, so i didn't get the full value in there.<BR>\n" );
document.write( "the rounding / truncating is usually good enough to get an accurate answer.\r<BR>\n" );
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document.write( "from the calculator, you can see that the confidence interval is the area between those two x-scores = .95.\r<BR>\n" );
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