Statistics: Population Proportions & Confidence Intervals?
Have I calculated the following problem correctly?
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= x/n = .013134, n=86,991, z=1.960, half width= .001
Upper confidence limit= .014
Lower confidence limit= .012
(b) Why is the normality assumption not a problem, despite the very small value of p?
The statistic p = x/n may be assumed normally distributed when the sample is large. The conservative rule of thumb says that normality may be assumed whenever np ≥ 10 and n(1 − π) ≥ 10. We can assume that p is normally distributed since np and n(1 − p) exceed 10.
