﻿ Fall 2010 Statistics 514 Exam 1 Take Home Questions

Stat 514      Fall 2010      Test 1       Take Home Questions

Bring these results and your calculations to the exam on October 1.  Show all work and keep answers on separate sheets, as you will not hand in all of the solutions.

1. A small random sample was taken of single-family house prices in Moscow, ID and Seattle, WA.  The prices are listed below (in thousands of dollars):

Moscow: 25.0, 238.9, 20.5, 429.9, 279., 138., 345.

Seattle: 789., 250., 579.5, 489.5, 749.9, 2395., 295., 1975.

a. Perform a t-test and a Wilcoxon test to see if prices differ between the two cities.

b. Perform an omnibus test of a difference in distributions between prices in the two cities.

c. Calculate the Hodges-Lehmann estimate of the shift parameter delta, and calculate a 95% confidence interval for delta. Verify the ka and kb values for the normal approximation by hand calculation.

d. Test for a difference in scale between the two house price distributions. Justify your choice of a scale test.

e. Calculate the number of elements in the permutation distribution for the differences between city house prices.

f. Give a brief summary of your results for parts a-d to describe if any differences were observed in these tests.  If any differences were detected, what do your results tell you about the house prices in the two cities?

2. In a paragraph (~5 sentences) make the argument for always using parametric (t-test) analyses for one or two sample problems.  Then in a second paragraph (~5 sentences) make the argument for always using nonparametric analyses for one or two sample problems.

3. Do problem 2.17 in the text.

4. Assume that the data for problem 1 are 15 house prices from a single city.

a. Perform a test of the hypothesis that the median price is 500 thousand dollars, versus the alternative that the median is greater than 500 thousand dollars.

b. Calculate a 95% confidence interval for the 75th percentile of the house price distribution.