Question 309132: 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.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
p-hat = 1143/86991 = 0.0131...
E = 1.96*sqrt[0.0131*0.9869/86991] = 7.556x10^-4
C.I. (p-hat-E,p-hat+E) = (0.0131,0.0131)
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(b) Why is the normality assumption not a problem, despite the very small value of p?
n is so large pn and qn both are greater than 5
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(Data are from Flying 120,
no. 11 [November 1993], p. 31.)
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Cheers,
Stan H.
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