Question

2.   An investigator for the FBI thinks that a real estate appraiser named Sunny is under-valuing properties so that wealthy people can avoid paying taxes on them. In an undercover operation, they pose as a wealthy client and ask Sunny to give a valuation on several properties. They also have an appraiser who works for the state, named Moon, give a valuation on the same properties. The summary statistics for both appraiser’s work are given in the table below. (Numbers are in millions of dollars.)

	prop 1	prop 2	prop 3	prop 4	prop 5	prop 6	prop 7	prop 8	prop 9
moon	5.59	6.06	4.33	5.28	5.97	1.95	7.9	3.71	3.07
sunny	3.97	4.67	3.25	4.12	4.3	1.42	6.24	2.82	2.3

a.   Will this be a matched pairs test, or a test for a difference in means from 2 separate groups? Explain briefly.
b.   Write hypotheses to check if Sunny’s mean valuation is significantly lower than Moon’s.
c.   Perform the calculations to test the hypotheses. Please report your test statistic (t) and your p-value.
d.   Is there strong evidence is Sunny is valuing properties significantly less than Moon?

Answer 1

a)

This is a matched pairs test because they both are dependent

b)

H0 : mud = 0
Ha: mud < 0

c)

moon   sunny   dbar
5.59   3.97   1.62
6.06   4.67   1.39
4.33   3.25   1.08
5.28   4.12   1.16
5.97   4.3   1.67
1.95   1.42   0.53
7.9   6.24   1.66
3.71   2.82   0.89
3.07   2.3   0.77

dbar = μ(before) - μ(after) = 1.077
s(dbar) = 0.5457

SE = s(dbar)/sqrt(n)  
= 0.5457/sqrt(9)
= 0.1819

Test Statisitcs, t = dbar/SE  
= 1.077/0.1819
= 5.9214

p value = .0002

d)

yes, there is strong evidence is Sunny is valuing properties significantly less than Moon