A study was made to compare the costs of supporting a family of four Americans for a year in different foreign cities. The lifestyle of living in the United States on an annual income of $75,000 was the standard against which living in foreign cities was compared. A comparable living standard in Toronto and Mexico City was attained for about $64,000. Suppose an executive wants to determine whether there is any difference in the average annual cost of supporting her family of four in the manner to which they are accustomed between Toronto and Mexico City. She uses the following data, randomly gathered from 11 families in each city, and an alpha of .01 to test this difference. She assumes the annual cost is normally distributed and the population variances are equal. What does the executive find?
|
Toronto
|
Mexico City
|
|
$69,000
|
$65,000
|
|
64,500
|
64,000
|
|
67,500
|
66,000
|
|
64,500
|
64,900
|
|
66,700
|
62,000
|
|
68,000
|
60,500
|
|
65,000
|
62,500
|
|
69,000
|
63,000
|
|
71,000
|
64,500
|
|
68,500
|
63,500
|
|
67,500
|
62,400
|
Use the data from the previous table to construct a 95% confidence interval to estimate the difference in average annual costs between the two cities.