Question 193656: In 1992, the FAA conducted 94,575 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 2,145 were positive.
(a) Construct a 99 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 the observed proportion (p)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In 1992, the FAA conducted 94,575 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 2,145 were positive.
(a) Construct a 99 percent confidence interval for the population proportion of positive drug tests.
p-hat = 2145/94575 = 0.0227
E = 2.5758*sqrt[0.0227*0.9773/94575) = 0.0012
99% C.I.: 0.0227 - 0.0012 < p < 0.0227 + 0.0012
99% C.I.: 0.0215 < p < 0.02395
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(b) Why is the normality assumption not a problem, despite the very small value of the observed proportion (p)
The sample size is very large.
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Cheers,
Stan H.
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