1. The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 50 Buffalo residents the mean is 22.5 miles a day and the standard deviation is 8.4 miles a day, and for an independent simple random sample of 40 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.4 miles a day.
a) What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?
b) What is the 95% confidence interval for the difference between the two population means?
c) Do these cities have the same population means? State the hypothesis and conclude using alpha = .05
2. A sample of 10 international telephone calls provided Sprint and WorldCom calling rates per minute for calls from the United States.
|
Country
|
Sprint
|
WorldCom
|
|
Australia
|
.46
|
.26
|
|
Belgium
|
.69
|
.40
|
|
Brazil
|
.92
|
.53
|
|
Colombia
|
.55
|
.53
|
|
Denmark
|
.50
|
.26
|
|
France
|
.46
|
.26
|
|
Germany
|
.46
|
.26
|
|
Hong Kong
|
.92
|
.40
|
|
Japan
|
.69
|
.40
|
|
United Kingdom
|
.46
|
.26
|
Provide a 95% confidence interval estimate of the difference between the two population means.
3. New York City, Boston, and Silicon Valley of California are among the areas with the highest technology salaries in the United States. The following sample data show individual annual salaries reported in thousands of dollars.
|
New York City
|
Boston
|
Silicon Valley
|
|
82
|
85
|
82
|
|
79
|
80
|
91
|
|
72
|
74
|
94
|
|
89
|
78
|
88
|
|
79
|
75
|
85
|
|
85
|
80
|
|
|
|
86
|
|
|
|
74
|
|
Use α = .05 and test for a significance difference among the population mean annual technology salaries for these locations. What is the p-value? What is your conclusion? If a difference exists, which location appears to have the highest mean technology salary?