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Math Help - Probability sample proportion

  1. #1
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    Probability sample proportion

    Hi!

    I've been wrestling with this the whole day, statistics is really not my forte.

    My problem is this:

    In a population of 4 260, 30.19 % are positive to a certain product.
    If I take a sample of 100, what is the probability that the proportion of people, in the sample taken, being positive to the product deviates max +/- 5 % from the proportion I got from the whole population (30.19 %).


    So far I have gotten this answer on formula structure:

    Pr{100(30.19%-5%) < X < 100(30.19%+5%) }
    I've also gotten that X ~ Binomial(100, 32.19%)


    However I have no idea how to use this. I need to be able to type a formula for the problem, calculate it and give the answers to it. We use SPSS as a program but from the question asked I believe I should be able to show the full calculations "by hand".

    I've tried with the binomial formula but my calculator can't handle 100!/(0.2519!(100-0.2519)!) ... Anyway the way I tried to interpret the answer I've gotten is to type:
    100!/(0.2519!(100-0.2519)!) * 0.3019^0.2519(1-0.6981)^100-0.2519 thereby trying to calculate the probability of the sample proportion being max -5 % below.
    I was then going to do the same for sample proportion being +5 % above and then just construct a Y<0.3019<X type interval as answer to the question. Am I way out in the blue here? Should I be using like z-tables or something instead?

    What is the name of the formula for this? My book mentions Binomial distribution (discrete distributions), Probabilities in a uniform distribution (continuous distribution), "Using the normal curve to approximate binomial distribution". All of these have varying formula to use and I can't really find one where I can calculate an interval of a deviation from population proportion %, being +/- 5 % in a sample of 100.

    As an edit:

    How do I calculate how big of a sample I need to take if there is a requirement that the Standard Deviation to the estimated proportion is at the most 2.5 %. If I use the proportion of people being positive to the product in the population (30.19 %)?

    Really grateful for any help!
    Last edited by Krapula; October 19th 2013 at 11:31 AM.
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  2. #2
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    Re: Probability sample proportion

    err typo in the second formula, it should say: X ~ Binomial(100, 30.19%)
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