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Math Help - [SOLVED] Sample St. Dev & Mean

  1. #1
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    [SOLVED] Sample St. Dev & Mean

    Okay, so I took Data Analysis I over half a year ago and now I'm in II and the Prof isn't really reviewing things in a way that is helping me. He's using software to teach so I don't really get what is going on (yeah, it's easy but come on...not good for learning) and I don't have my old book to review with since I left it at home over the summer. I feel so nervous, I can't recall this stuff and I don't have the software to breeze through it anyways. Here is what I'm stuck on:

    A random sample is to be selected from a population that has a proportion of successes π = 0.61. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes. (Round the answers for μp to two decimal places, the answers for σp to four decimal places.)

    1. n = 30
    μp =
    σp =


    If someone can help me figure out that one there, hopefully it'll come back to me and I can do the rest. I just can't remember this for the life of me.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I have trouble understanding this notation, but here goes.

    In estimating the true proportion or say the probability of an event, p.
    Which I think is your \pi...

    You sample n data points.
    The proportion of successes from the data is

    \hat P={Y\over n}

    where Y is a binomial random variable with n number of trials and success probability our p.

    \hat P={Y\over n} is unbiased meaning that E(\hat P)={E(Y)\over n}={np\over n}=p

    and variance of \hat P is {p(1-p)\over n}

    SO plug in that value of Pi for my p and also the value for n.
    Note that a standard deviations is the square root of the variance.
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