Data gathered by the U.S Department of Transportation show 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 100 Boston residents the mean is 18.6 miles a day and the standard deviation is 7.4 miles a day.
i. 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?
ii. What is the 95% confidence interval for the difference between the two population means?
iii. Are all the requirements to build a confidence interval for the differences of mean satisfied?