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Math Help - Confidence Interval Question

  1. #1
    sweet_gurl
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    Exclamation Confidence Interval Question

    Hi,

    I was hoping that someone could help me with the following question by showing me how to do it using confidence intervals. Although I've done it using the standard error, I want to know how to do it using confidence intervals, but I'm not sure how, as we are not given the sample mean (x bar).

    Experience with workers in a certain industry indicates that the time required for a randomlyselected worker to complete a job is approximately normally distributed with a standarddeviation of 12 minutes. If the sample mean is calculated as an estimate of the mean of allworkers, what is the relative accuracy of a measure based on a sample of 64 workers comparedwith one based on a sample of 16 workers?

    Thank you very much!

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  2. #2
    MHF Contributor
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    n\;=\;\frac{z^{2}s^{2}}{d^{2}}\;\implies\;d\;=\;\f  rac{s*z}{\sqrt{n}}

    Then \frac{d_{16}}{d_{64}}\;=\;\frac{\frac{s*z}{\sqrt{1  6}}}{\frac{s*z}{\sqrt{64}}}\;=\;\frac{\sqrt{64}}{\  sqrt{16}}\;=\;\frac{8}{4}\;=\;2
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