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Math Help - confidence interval help!!!!

  1. #1
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    Exclamation confidence interval help!!!!

    how do you find a confidence interval without knowing the mean or standard deviation?!

    If it helps, here is the question being asked
    "construct a 95% confidence interval for the following:
    N=100
    N=1,000
    N=10,000
    Use a sample proportion of .4 throughout."
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  2. #2
    Super Member Aryth's Avatar
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    Use the following equations:

    p \approx \hat{p} = 0.4

    CI = \hat{p}\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}

    All we need to find now is z_{\frac{\alpha}{2}}

    We are given 0.95, so we just use the following:

    (1 - \alpha) = 0.95

    \alpha = 0.05

    This is a common alpha, and has the corresponding z_{\alpha} and z_{\frac{\alpha}{2}} values:

    z_{\alpha} = 1.645

    z_{\frac{\alpha}{2}} = 1.96

    All you do now is plug and go.

    I'll do the n = 100 for you:

    CI+ = 0.4 + 1.96\sqrt{\frac{0.4(0.6)}{100}}

    CI+ = 0.4 + 1.96\frac{\sqrt{0.24}}{10}

    CI+ = 0.4 + 1.96\frac{0.49}{10}

    CI+ = 0.4 + 1.96(0.049)

    CI+ = 0.4 + 0.0964 = 0.4964

    CI- = 0.4 - 0.0964 = 0.3036

    So, your CI is between 30.3 and 49.64 percent.

    Just do this again for 1000 and 10000.
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