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Statistics with confidence intervals

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose the porosity (in %) of samples taken from the ground found to be normally distributed with σ = 0.85 %

    What sample size is necessary to estimate the true mean porosity to within 0.25
    with 99% confidence?

    2. Relevant equations

    C.I. = confidence interval = mean +- z*σ*n^(-0.5)
    n = (2*z*σ/w)^2
    interval width = w
    z = 2.575

    3. The attempt at a solution

    Not really sure what is meant by "... to within 0.25" maybe someone can help clarify this? Is it referring to the confidence interval width? Also, I thought that the confidence intervals do not estimate the true mean. I thought C.I. only estimates whether or not the other samples will have the same mean within the C.I. range.
     
    Last edited: Jun 16, 2009
  2. jcsd
  3. Jun 17, 2009 #2

    statdad

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    Usually "to within xxx" refers to the desired margin of error - this would not be the length of the confidence interval, but half the length.

    A confidence interval provides a range of values which can be considered "reasonable values" for the true mean (that is highly non-mathematical language, but I think it gets the point across)
     
  4. Jun 17, 2009 #3
    thanks for clarifying the problem statdad.
     
  5. Jun 17, 2009 #4

    EnumaElish

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    0.25 is the interval width ("w"), which is the same as error margin. This can be interpreted as ±0.25. Since it was not stated as ±0.25 but as 0.25, they probably meant ±0.125.

    The 99% C.I. implies a 0.5% probability under either tail, as statdad suggested. You should verify that your z value is consistent with that probability.
     
    Last edited: Jun 17, 2009
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