document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184292>Question 184292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120,no. 11 [November 1993], p. 31.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138334 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=138334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive<BR>\n" );
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document.write( "The sample proportion is 1143/86991 = 0.01314<BR>\n" );
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document.write( "(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.<BR>\n" );
document.write( "E = z*sqrt(pq/n)<BR>\n" );
document.write( "E = 1.96*sqrt(0.01314*0.98686/86991) = 0.000757<BR>\n" );
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document.write( "95% CI: 0.01314-0.000757 < p < 0.01314+0.000757<BR>\n" );
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document.write( "(b) Why is the normality assumption not a problem, despite the very small value of p? <BR>\n" );
document.write( "n is large<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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