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Unformatted text preview: Estimators, Estimates, and Sampling distributions Examples 1. Suppose that we use the Normal distribution to model the heights of females in the United states. Lets assume that this Normal distribution has mean = 65 inches and standard deviation = 3 inches. (a) If we plan to take a random sample of size n , specify the probability distribution of the sample mean X , (give the distribution name and specify its parameters) (b) If we plan to take a random sample of size n = 20, what is the probability that we will observe a sample mean within 2 inches of the mean = 65 inches. (c) Compute and compare the standard deviation of the sample mean X for the cases n = 10 and n = 50. (d) Compute and compare the standard deviation of the sample mean based on a random sample of size n = 10 for the cases when the standard deviation of the Normal distribution used to model the heights of females is = 3 and = 8. 2. The following observations: x 1 ,x 2 ,...,x 24 are a realization of a random sample X 1 ,X 2 ,...,X 24 from a Normal distribution (generated using Rs random number gen- erator)....
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