Suppose that a college professor lives 65 miles from campus and is interested in the average time it takes her to commute to work each morning. Driving the same route each day, she records the time it takes her to get to work (in minutes) on 20 randomly selected days. Because there is construction on the route that she usually takes, there are days when it takes much longer than others to get to work. A histogram of the data shows that the data are skewed to the right. The information provided below shows the confidence intervals for the mean time to get to work using (A) raw (untransformed) data, and (B) log-transformed data, which showed a more normally distributed data set.
Calculate the width of both intervals in the original units of minutes (note that you will need to convert the log-transformed interval back into minutes). Which interval is narrower?
◦ Width of interval for untransformed data: 5.60; width of interval for transformed data: 6.53. The width of the interval for the untransformed data is narrower.
◦ Cannot be determined with the given information
◦ Width of interval for untransformed data: 5.60; width of interval for transformed data: 5.02. The width of the interval for the log transformed data is narrower.
◦ Width of interval for untransformed data: 5.02; width of interval for transformed data: 5.60. The width of the interval for the untransformed data is narrower.
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