Question 251868: I dont know how to utilize 95% confidence and how it works in the problem, thank you!
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?
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.
sample proportion: 1143/86991 = 0.013
standard error: 1.96*sqrt[0.013*0.987/86991] = 0.0003841
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95 CI: 0.013-0.0003841 < p < 0.013+0.000384
95 CI: 0.0126 < p < 0.0134
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(b) Why is the normality assumption not a problem, despite the very small value of p?
I'll leave that to you. I would say something about the large sample size.
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Cheers,
Stan H.
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