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Question 153494: 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? : 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(18999) About Me  (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.
p-hat = 1143/86991 = 0.013139
sigma = sqrt[p'q'/n'] = sqrt[0.013*0.0.987/86991]= 0.000384...
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(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.
E = 1.96*0.000384 = 0.000753..
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95% C.I.: 0.013-0.000753 < p < 0.013 + 0.000753
95% C.I.: 0.0122 < p < 0.013763
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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.
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Cheers,
Stan H.