All maximum possible random samples of size 4 are drawn from the finite population comprisi of X=3,5,7. a) Verify central limit theorem (CLT) in this random experiment b) Between what two sample means would you expect the a. Middle 68% of sample means to fall
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- Suppose we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birth weights are different from normal. To test this hypothesis, a random sample of 100 birth weights is selected from a list of full-term babies of SES mothers. The mean birth weight is found to be 115 oz. Suppose the average birth weight of all babies (based on nationwide surveys of millions of deliveries) is known to be 120 oz with = 24 oz. Set = .05 Assume all conditions are met, what is the p-value of their test? Give your answer to 4 decimal places.A researcher plans to select a random sample from a population with o=20 what is the minimum sample size the researcher needs to have a standard error no greater than 2 points?A certain factory produces Xn specialized parts on day n, where Xn are independent and identically distributed random variables with mean 6 and variance 9. Let Sn be the total number of specialized parts produced from day 1 to day n. Using central limit theorem, determine the total number of parts, a, the said factory can guarantee to produce by day 50 with at least 99.9% certainty, i.e. determine the maximum value of a so that P(S50≥a)≥0.999. Note: This maximum value must be a whole number.