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Math Help - Confidence interval question

  1. #1
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    Confidence interval question

    Hi
    The following question i am having difficulties solving.

    In certain water-quality studies, it is important to check for the presence or absence of various types of micro-organisms. Suppose that 20 out of 100 randomly selected
    samples of a fixed volume show the presence of a particular micro-organism.
    (a) Estimate the true probability of finding this micro-organism in a sample of the
    same volume, using a 95% confidence interval.

    i know that 20/100 = .20 shows the presence of a particular micro-organism and .80 does not.

    the confident interval is .95%

    so i get something like this

    .20 + 1.95 * \sqrt(.20*.80/100)

    however this is incorrect

    (b) Can it reasonably be said that there is only a 10% chance that a sample of the
    given volume will contain the micro-organism?

    P.S
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  2. #2
    MHF Contributor matheagle's Avatar
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    Re: Confidence interval question

    would 1.96 instead of the 1.95 give you the correct answer?
    1.96 is right, but your error is minimal.
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  3. #3
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    Re: Confidence interval question

    the answer is for 8a) (0.1216,0.2784)

    edit: got the correct answer
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  4. #4
    MHF Contributor matheagle's Avatar
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    Re: Confidence interval question

    that is correct with 1.96 used as the approximate percentile point
    this is a normal approximation to the binomial distribution
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