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Fashion Industries: Applicants Condition of Employment

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As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants 14 failed the test. Develop a 99 percent confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10 percent of the applicants are now failing the test? In addition to the testing of applicants,Fashion Industries randomly tests its employees throughout the year. Last year in the 400 random tests conducted, 14 employees failed the test. Would it be reasonable to conclude that less than 5 percent of the employees are not able to pass the random drug test?

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Solution Summary

Formula, calculations and answers are provided for calculating the confidence interval.

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(a) p = 14/220 = 0.06364, q = 1 - p = 0.9364
SE = sqrt(pq/n) = sqrt(0.06364 * 0.9364/220) = 0.0164
For 99% confidence, z = 2.576
The 99% CI for the proportion of applicants who fail the test is given by
[p - z * SE, p + z * SE] = ...

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