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):
What is the decision at the 5% level of significance?
A) Fail to reject the null hypothesis and conclude that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa.
B) Since the P-value is less than the t-stat we conclude that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa.
C) Since the P-value is so very small, we conclude that the average house prices in East Vancouver are indeed at least $60,000 greater than those in Oshawa.
D) Conclude that the average house prices in East Vancouver are different than those in Oshawa.

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):
 What is the decision at the 5% level of significance?
A) Fail to reject the null hypothesis and conclude that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa. 
B) Since the P-value is less than the t-stat we conclude that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa. 
C) Since the P-value is so very small, we conclude that the average house prices in East Vancouver are indeed at least $60,000 greater than those in Oshawa. 
D) Conclude that the average house prices in East Vancouver are different than those in Oshawa.

Quizplus · Accepted Answer

The hypothesis test is a one-sided t-test with a null hypothesis that the average house prices in East Vancouver are not more than $60,000 greater than those in Oshawa. The alternative hypothesis is that the average house prices in East Vancouver are indeed at least $60,000 greater than those in Oshawa. The test statistic is calculated as (mean_EV - mean_Oshawa - $60,000) / (s / sqrt(n)), where mean_EV is the sample mean of house prices in East Vancouver, mean_Oshawa is the sample mean of house prices in Oshawa, s is the pooled standard deviation, and n is the sample size. The degrees of freedom are calculated as (n1 - 1) + (n2 - 1) = 17. The t-statistic is calculated as (1.88 - 1.1 - 0.06) / (0.779 / sqrt(9 + 9)) = 6.14. The P-value is less than 0.001, which is very small. Therefore, we reject the null hypothesis and conclude that the average house prices in East Vancouver are indeed at least $60,000 greater than those in Oshawa.

The Employees at the East Vancouver Office of a Multinational