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Math Help - Confidence Interval problem.

  1. #1
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    Confidence Interval problem.

    I'm having trouble figuring out this question.

    Suppose that we are interested in buying ball bearings from a certain manufacturer. We require very precisely manufactured ball bearings, and so we decide to investigate this manufacturer's output. In a random sample of 400 of the ball bearings, 48 of them contain manufacturing defects that make them useless to us.
    What is a 95% confidence interval for the population proportion of defective balls?
    a).12+ 0.0288
    b).12+ 0.0298
    c).12+ 0.0308
    d).12+ 0.0318
    e).12+ 0.0328

    I'm using the equation: .12+ 1.96 * (stnd dev./ square root of n)
    I estimated 2.4 as the standard deviation in the question before, but I think that might be wrong.

    Also What is the 99% margin of error? I have no clue how to figure that out.

    Some guidance on how to at least start this question/equation would be great.
    Last edited by jhallett17; February 17th 2011 at 10:55 AM.
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  2. #2
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    I would say

    \displaystyle p\pm Z\times \sqrt{\frac{p(1-p)}{n}} = 0.12\pm 1.96\times \sqrt{\frac{0.12(1-0.12)}{400}} = 0.12\pm 0.0318
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