Question

22. As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 400 applicants, 30 failed the test.

1. Develop a 95% confidence interval for the proportion of applicants that fail the test.

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2. Would it be reasonable to conclude that 6% of applicants fail the drug test? Explain why or why not.

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Answer 1

a)

sample proportion, = 0.075
sample size, n = 400
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.075 * (1 - 0.075)/400) = 0.0132

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0132
ME = 0.0259

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.075 - 1.96 * 0.0132 , 0.075 + 1.96 * 0.0132)
CI = (0.049 , 0.101)

b)
No, it would not be reasonable, because confidence interval contains 6%