00:01
A direct mail company wants to estimate the proportion of people who will purchase a product.
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We are given the true population proportion.
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It's 0 .07.
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Their sample size is 343.
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We want the probability that when they take their sample, their sample proportion will be less than 0 .11.
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Probability p -hat below 0 .11.
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So how do we find this? well initially, if you look at this, we have a binomial distribution.
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343 independent trials, two outcomes, they purchase or they don't, same probability p for each.
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And this is a binomial with variable x, the number of people in the sample who do make a purchase.
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We're going to take a normal approximation.
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So we now have something approximately normal.
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It still represents x.
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Its mean is np.
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Its standard deviation is root np, 1 minus p.
01:01
These are just the mean and standard deviation of the binomial.
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Now to turn this into a distribution of p -hat, the sample proportion, i just divide by n...