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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Definitions:

Directly Address

To confront or deal with a matter openly and straightforwardly.

Different Time

A period distinct from the present, often implying a change in circumstances, environments, or conditions.

Confidentiality

The obligation to keep personal, medical, or official information secret and not to disclose it to unauthorized individuals.

Surveys

Research methods that collect data from a specific population to study opinions, behaviors, or characteristics, typically through questionnaires or interviews.