| Question : In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security relatd jobs and found that 1,143 were positive a. construct a 95% confidence interval for the population proportion of positive drug test. b. why is the normality assumption not a problem, despite the very small value? Answer : Use the confidence interval around a proportion calculator to construct a 1-sample binomial confidence interval. With a sample size as large as 86k the normal Wald confidence interval and Adjusted-Wald intervals will be virtually identical (to a few decimal places). The 95% CI is between 1.24% and 1.39%. The normality assumption is not a problem since while distribution here is binomial, the Central limit theorem shows that as sample sizes get larger (in this case very large) the binomial distribution begins to resemble the normal distribution. | How helpful was this answer?
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