The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):
Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
What is the value of calculated t?
A) +1.93
B) +3.22
C) -2.76
D) -2.028

Question

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $1000, rounded to the nearest thousand):
 Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000?
What is the value of calculated t?
A) +1.93 
B) +3.22 
C) -2.76 
D) -2.028

Quizplus · Accepted Answer

We need to conduct a two-sample t-test since we are comparing the means of two different populations (East Vancouver and Oshawa). Using the given data, we find that the sample mean of East Vancouver houses is $790,000 and the sample mean of Oshawa houses is $727,000. The difference in sample means is $63,000. We also calculate the standard deviations of the two samples to be $101,000 for East Vancouver and $70,000 for Oshawa. 
Using a two-sample t-test with unequal variances and a significance level of 0.05, we find a calculated t-value of 3.22. This value falls in the rejection region of the t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 14). Therefore, we can conclude that the difference between the population means is significantly greater than $60,000.

The Employees at the East Vancouver Office of a Multinational