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##### UCSB PSTAT 109 Statistics for Economics Quiz7 Winter 2014

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Question;PSTAT 109: Quiz 7;Winter 2014;Instructions: Please show all formulas and calculations in;an organized fashion for full credit.;Problem 1. For the;following data;21, 18, 17, 23, 22, 19, 21, 17, 25;compute the following measures;a. mean;b. sample variance;c. the 30th percedntile;d. the median;e. the 83rd percentile;In general, what is the advantage of reporting the median;value as opposed to the mean value?;Problem 2.Suppose;X1 and S 2 1 are the sample mean and sample variance from a population with;mean 1 and variance2;1, and X 2 and S 2 2 are the sample mean and sample variance from a second;independent population with mean 2 and 2;The sample sizes are;n1 and n2, respectively. Show that..;b. Now suppose we have the same setup as in (a) but 2 1 =2 2 =2. Show that the pooled sample variance;is an unbiased estimator of 2. (Hint: Sample variance S 2 is;an unbiased estimator of population variance2.);Problem 3.;Candidate A is running for student body president at some university. The proportion;of students who favor this candidate at the moment is 0.8.;a. Suppose a simple random sample of 100 students is taken.;What are the expected value, standard deviation, and shape of the sampling;distribution of p?;b. If a simple random sample of 100 students is taken, what;is the probability that the number of students in the sample who DO NOT favor;Candidate A will be between 26 and 30?

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