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Math Help - population proportion

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    population proportion

    The Coca-cola Company has 40% of the cola market. The probability that a sample proportion for n=30 falls within 0.10 of the true population proportion of .40, which represents the proportion of cola drinkers who prefer a coca-cola drink is?
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    Quote Originally Posted by jax760 View Post
    The Coca-cola Company has 40% of the cola market. The probability that a sample proportion for n=30 falls within 0.10 of the true population proportion of .40, which represents the proportion of cola drinkers who prefer a coca-cola drink is?
    z_{\alpha/2} \sqrt{\frac{(0.4)(0.6)}{30}} = 0.10.

    Solve the above equation for the critical value z_{\alpha/2} and hence get the value of \alpha. Use this value to get the required probability.

    eg. If z_{\alpha/2} = 1.96 then (using tables) \frac{\alpha}{2} = 0.025 \Rightarrow \alpha = 0.05 and so the required probability would be 0.95.
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