Question

Consider two series of ratios of "municipal evaluation" over "sale prices", corresponding respectively to data available for uni-family houses and multi-families houses. It is assumed that the samples are taken from populations with equal variances.

The first series consists of 10 ratios from the uni-family houses where:

x1=0.867           S1=0.1674

The second series consists of 9 ratios from the multi-families houses where:

x2=0.653           S2=0.2907

1. Construct a confidence interval at the level 1-α=0.95 to estimate the difference in the means of the above-mentioned variable for these two housing categories.
2. What are the assumptions, concerning the populations, which should be respected in order to proceed with the inferences requested in (a)?

Answer 1

(a)

n1 = 10

1 = 0.867

s1 = 0.1674

n2 = 9

2 = 0.653

s2 = 0.2907

Pooled Standard Deviation is given by:

df = 10 + 9 - 2 = 17

= 0.05

From Table, critical values of t = 2.11

Confidence Interval:

Answer is:

(-0.013, 0.441)

(b)

the assumptions, concerning the populations, which should be respected in order to proceed with the inferences requested in (a) :

(i) The two populations have the same variance. This assumption is called homogeneity of variance.

(ii) The populations are normally distributed.

(iii) Each variable is sampled independently from each other value.