Suppose the manager of a large furniture store wants to estimate the amount spent by customers during the holiday season. She took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left-skewed. The figures below show the confidence intervals for the mean amount spent using (A) raw (untransformed) data, and (B) log-transformed data, which showed a more normally distributed data set. Use this information to answer the question.
Calculate the width of both intervals (note that you will need to convert the log-transformed interval back into dollars). Which interval is narrower?
◦ Width of interval for untransformed data: 144.2; width of interval for transformed data: 152.5. The width of the interval for the untransformed data is narrower.
◦ Cannot be determined with the given information
◦ Width of interval for untransformed data: 144.2; width of interval for transformed data: 129.8. The width of the interval for the log transformed data is narrower.
◦ Width of interval for untransformed data: 72.1; width of interval for transformed data: 273. The width of the interval for the log transformed data is narrower.
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