Question

A real estate agent wishes to determine whether tax assesso s and real estate appraisers agree on the values of homes. A random sample of the two g oups appraised 10 homes. Is there a significant difference in the values of the homes for each group? Let a = 0.05. Assume the data are from normally distributed populations.

 

Reference Points

x

s

n

Starting Salaries

Real Estate Appraisers

php 83 256

php 3256

10

Tax Assessors

php 88 354

php 2341

10

Answer 1

$\bar x_1=83256,s_1=3256,n_1=10,\\ \bar x_2=88354,s_2=2341,n_2=10.$

Our null hypothesis is that the values of the homes for each group are the same:

$H_0:\mu_1=\mu_2.$

The alternative hypothesis is that the means are not equal:

$H_1:\mu_1\ne\mu_2.$

We calculate the pooled standard deviation:

$s_p^2=\cfrac{((n_1-1)s_1^2+(n_2-1)s_2^2)}{n_1+n_2-2}=\\ =\cfrac{((10-1)\cdot 3256^2+(10-1)\cdot 2341^2)}{10+10-2}=\\ =8040908.5;\\ s_p=\sqrt{8040908.5}=2835.6.$

Next, we calculate the test statistic t:

$t=\cfrac{\bar x_1-\bar x_2}{s_p\sqrt{1/n_1+1/n_2}}=\\ =\cfrac{83256-88354}{2835.6\sqrt{1/10+1/10}}=-4.0201.$

Using the t-table we find the t-value with α = 0.05 and 18 degrees of freedom

(df = n₁+ n₂ - 2 = 10 + 10 - 2 = 18):

$t_{0.05;18}=1.734.$

The test statistic is higher than the t value. We reject the hypothesis of equal means, there is a significant difference in the values of the homes for each group.