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    zetablue1's Avatar
    zetablue1 Posts: 28, Reputation: 1
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    #1

    Mar 20, 2010, 06:06 PM
    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.
    Chris-infj's Avatar
    Chris-infj Posts: 31, Reputation: 4
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    #2

    Mar 21, 2010, 09:51 AM

    Calculations OK. 95% Confidence interval is [0.0124, 0.0139] or the numbers you rounded off to.
    zetablue1's Avatar
    zetablue1 Posts: 28, Reputation: 1
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    #3

    Mar 22, 2010, 08:26 PM
    Quote Originally Posted by Chris-infj View Post
    Calculations ok. 95% Confidence interval is [0.0124, 0.0139] or the numbers you rounded off to.
    Thanks for your help.
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