Question

The book’s Atlanta Commute (distance) dataset (available directly on StatKey) provides
the commute distances in miles for 500 randomly chosen people who work in the Atlanta
metropolitan area.
(a) Use StatKey to obtain the mean and standard deviation of the commute distances in this
sample.
(b) Use StatKey to create 5000 bootstrap samples and a bootstrap distribution of sample
means. What are the mean and standard error of your bootstrap distribution?
(c) Use your bootstrap distribution to determine 95% and 99% confidence intervals for the
average commute distance of workers in the Atlanta metropolitan area. Determine the
margin of error for each of these confidence intervals. What happens to the margin of
error as the confidence level increases?
(d) Based on your bootstrap distribution and your interval estimates, which of the following
is most likely and which is least likely?
i. the average commute distance for people who work in the Atlanta metropolitan area
is less than 20 miles
ii. the average commute distance for people who work in the Atlanta metropolitan area
is around 20 miles
iii. the average commute distance for people who work in the Atlanta metropolitan area
is greater than 20 miles
Explain.

Answer 1

(a) The mean is 18.156.

The standard deviation is 13.798.

(b) The mean is 17.712.

The standard error is 0.598.

The StatKey output is:

(c) The 95% confidence interval for the average commute distance of workers in the Atlanta metropolitan area is between 16.54 and 18.89 with the margin of error of 1.18.

The 99% confidence interval for the average commute distance of workers in the Atlanta metropolitan area is between 16.17 and 19.26 with the margin of error of 1.55.

As the confidence level increases, the margin of error increases.

(d) (i) The average commute distance for people who work in the Atlanta metropolitan area is less than 20 miles is least likely.

(ii) The average commute distance for people who work in the Atlanta metropolitan area is around 20 miles is least likely.

(iii) The average commute distance for people who work in the Atlanta metropolitan area is greater than 20 miles is most likely.

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