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 k_{a} and k_{b} 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 75^{th}
percentile of the house price distribution.