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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online