Use the Following Information to Answer the Question -Choose the Statement That Explains Which Confidence Interval Is Likely

question 43

Multiple Choice

Use the following information to answer the question. Suppose the manager of a large high-end jewelry 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. $$\begin{array}{l}\begin{array} { | l c c c c c | } \hline { \text { (A) One-Sample T: Purch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { Purch } & 15 & 223.5 & 100.4 & 26.0 & ( 167.9,279.1 ) \\\hline\end{array}\\\\\begin{array} { | l c c c c c | } \hline { \text { (B) One-Sample T: LogPurch } } \\\hline \text { Variable } & \text { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { LogPurch } & 15 & 2.311 & 0.236 & 0.101 & ( 2.2,2.4 ) \\\hline\end{array}\end{array}$$
-Choose the statement that explains which confidence interval is likely to be a more precise estimate of amount spent and why.

• A) The confidence interval for the geometric mean is more precise because the distribution of the log-transformed data is more symmetric.
• B) The confidence interval for the untransformed data is more precise because the values are in
• Actual dollars which is more meaningful.
• C) The confidence interval for the untransformed data is more precise because it is strongly
• Left-skewed and the confidence interval gives a wider interval.
• D) None of these.

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