Question

The Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective home buyers in the Southlake and Northwood areas of the city looking at small samples comparing µ1 to µ2. One item if interest is the length of time the seller occupied the home. A sample of 14 homes sold recently in Southlake revealed that the mean length of ownership was 7.4 years where s = 2.3 years. A sample of 28 homes in Northwood revealed that the mean length of ownership was 9.1 years with s equaling 2.9 years. Can we conclude that the Northwood residents owned their homes for a longer period of time compare to residents in the Southlake area? α = 0.05.

Answer 1

We can conclude that there is significant evidence that Northwood residents owned their homes for a longer period of time compare to residents in the Southlake area

Explanation:

H0 : μ1 = μ2

H1 : μ1 < μ2

Given :

n1 = 14 ; n2 = 28

x1 = 7.4 ; x2 = 9.1

s1 = 2.3 ; s2 = 2.9

α = 0.05

Test statistic :

(x1-x2) ÷ sqrt[(((n1-1)*s1² + (n2-1)*s2²) ÷ df) * (1/n1+1/n2)]

(7.4 - 9.1) ÷ sqrt[(((13*2.3^2) + (27*2.9^2)) ÷ 40) * (1/14 + 1/28)]

t = -1.7 ÷ sqrt[((68.77 + 227.07) / 40) * 0.1071428]

t = -1.7 ÷ sqrt(0.7924281488)

t = - 1.7 ÷ 0.8901843

t = - 1.909

t = - 1.91

The Pvalue :

P(t < - 1.91) = 0.028067

At α = 0.05 ;

Pvalue < α ; We reject the Null

We can conclude that there is significant evidence that Northwood residents owned their homes for a longer period of time compare to residents in the Southlake area