PS 7 full - ECON 2843 Problem Set 7 1. Problem 8.2 in...

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ECON 2843 Problem Set 7 1. Problem 8.2 in Newbold on p. 260-261. A random sample of eight homes in a particular suburb had the following selling prices (in thousands of dollars). 92 83 112 127 109 96 102 90 a. Find a minimum variance unbiased point estimate of the population mean? b. Use an unbiased estimation procedure to find a point estimate of the variance of the sample mean? c. Use an unbiased estimator to estimate the proportion of homes in this suburb selling for less than $92,500? 2. Problem 8.4 in Newbold on p. 261. Let X 1 and X 2 be a random sample of observations from a population with mean μ and variance σ 2 . Consider the following three point estimators, X, Y, Z, of μ . X = (1/2) X 1 + (1/2) X 2 Y = (1/4) X 1 + (3/4) X 2 Z = (1/3) X 1 + (2/3) X 2 a. Show that all three estimators are unbiased. b. Which of the estimators is the most efficient? c. Find the relative efficiency of X with respect to each of the other two estimators. 3. Problem 8.8 in Newbold on p. 269. A college admissions officer for an M.B.A. program has determined that historically, applicants have undergraduate grade point averages that are normally distributed with standard deviation 0.45. From a random sample of 25 applications from the current year, the sample mean grade point average is 2.90. a. Find a 95% confidence interval for the population mean. b. Based on these sample results, a statistician computes for the population mean a confidence interval extending from 2.81 to 2.99. Find the confidence level associated with this interval. 4. Problem 8.9 in Newbold on p. 269. A process producing bricks is known to give output whose weights are normally distributed with standard deviation of 0.12 lb. A random sample of 16 bricks from today’s output had mean weight of 4.07 lb. a. Find a 99% confidence interval for the mean weight of all bricks produced this day.
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This note was uploaded on 04/07/2008 for the course ECON 2843 taught by Professor Hudgins during the Spring '08 term at The University of Oklahoma.

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PS 7 full - ECON 2843 Problem Set 7 1. Problem 8.2 in...

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