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    Help with simple CI for proportion using SRS




    I'm having difficulty with the following problem:

    Imagine you are a gerontologist who is interested in investigating the proportion of households that contain at least one person over age 70 in the town of Jillwood. Jillwood has 800 households according to the post office. A SRS of 60 household was selected from the post office list. Out of 60 households surveyed, 12 were found to have at least one person over the age of 70. Compute the 95% CI for the proportion of household in the Jillwood population that contain a persona over the age of 70, and then write a corresponding sentence to state your findings.

    This is the relevant formula I was given for computation:
    95% CI=p +or- 1.96xsquare root of (1-f)(S2p)

    S2p=px(1-p)/n-1, p=# w/ person over 70/n, f=n/N

    So I got the following:
    p=.2
    f=.075
    S2p=.0145

    After I plugged that into the relevant formula, I got a 95% CI of [.427, -.027].

    How can that be so? How can I have a negative CI? What am I doing wrong?

    I've consulted my text and readings from my prof. I've also been looking at other stat websites online...

    Thanks for your help!

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    Re: Help with simple CI for proportion using SRS

    I used the same formula. I didn't get a negative. n=60, N=800?
    "I have discovered a truly remarkable proof of this theorem which this margin is too narrow to contain." Pierre de Fermat

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    Re: Help with simple CI for proportion using SRS

    Yes, n=60, N=800. Therefor, if f= n/N, then f=.075. Do you have the same f, p, and S2p results? Is that where the error is or is it after I plug those into the formula?

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    Re: Help with simple CI for proportion using SRS

    I really just want to know where the error is, not what the answer is.

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    Re: Help with simple CI for proportion using SRS

    s2p= \frac{(0.2)(0.8)}{59} based on your formula. I get 0.0027

    But even with your value, I don't think you'd get a negative.

    1.96\sqrt{(0.925)(0.0027)} If I'm interpreting the formula right.
    Last edited by Buckeye; 10-09-2016 at 12:22 AM.
    "I have discovered a truly remarkable proof of this theorem which this margin is too narrow to contain." Pierre de Fermat

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    Re: Help with simple CI for proportion using SRS


    Agh! You're right. I see my error. I entered 12 (# of people over 70) as the n into the denominator (n-1) instead of 60. Pretty simple error. Thank you!!

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