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Unformatted text preview: Chapter 4: Sampling Distribution Models Statistics that we calculate from data are functions of random variables and so have different distributions than the population that we drew them from. We will rely on the properties of sample means and variances that we learned earlier to derive the sampling distributions of some important statistics that we use to estimate population parameters. Sampling Distribution for Proportions If we are interested in estimating a population proportion, what would you guess would be a good estimator we could calculate from our data? That is, if we want to estimate the parameter p from a binomial, what would be a plausible sample statistic, ? p ˆ Example : Suppose that 70% of all Florida adults approve of Bush’s handling of the situation in Iraq. Simulate a random sample of size n = 10 from this population using the table of random digits with a “random” starting place. Compute , the proportion of your sample who approve of Bush’s handling of the situation. p ˆ Collecting the results of many repetitions of this simulation approximates the sampling distribution of for n = 10. p ˆ With the computer, we can simulate thousands of random samples of size 10 or any other size. Compare the sampling distributions of for sample sizes 10, 25 and 100 – center, spread, and shape. p ˆ The simulations verify the following results that can be proved theoretically about the sampling distribution of for simple random samples of size n from a population with proportion p : p ˆ • The mean of the sampling distribution of is p . p ˆ • The standard deviation of the sampling distribution of is p ˆ n pq where q = 1 –...
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