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 compared to residents in the Southlake area? Test at α = 0.05. Neighborhood Sample size Mean Years in home Std deviation (Years) Southlake 14 ×̅1 = 7.4 2.3 Northwood 28 ×̅2 = 9.1 2.9

• A. 1 tail 1.645, 6.396

• B. 1 tail, 1.645, -1.7

• C. 1.684, -1.91, 1 tail

• D. 2 tail, 1.684, 1.91

• E. 1 tail, 1.684, -1.91

Answer 1

For Sample 1 :

x̅1 = 7.4, s1 = 2.3, n1 = 14

For Sample 2 :  

x̅2 = 9.1, s2 = 2.9, n2 = 28

α = 0.05

Null and Alternative hypothesis:

Ho : µ1 = µ2 ; H1 : µ1 > µ2

It is one-tailed test.

df = n1+n2-2 = 40

Critical value, t crit = ABS(T.INV(0.05, 40)) = 1.684

Pooled variance :

S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2) = ((14-1)*2.3² + (28-1)*2.9²) / (14+28-2) = 7.3960

Test statistic:

t = (x̅1 - x̅2) / √(s²p(1/n1 + 1/n2 ) = (7.4 - 9.1) / √(7.396*(1/14 + 1/28)) = -1.91

Answer E.

It is one tailed test.

Critical value = 1.684

Test statistic = -1.91