Use the Following Information to Answer the Question -Choose the Statement That Explains Which Confidence Interval More Precisely

question 21

Multiple Choice

Use the following information to answer the question. 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. $$\begin{array}{l}\begin{array} { | l l l l l c | } \hline { \text { (A) One-Sample T: Purch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { Purch } & 17 & 544.5 & 140.2 & 26.0 & ( 472.4,616.6 ) \\\hline\end{array}\\\\\begin{array} { | l c c c c c | } \hline { \text { B) One-Sample T: LogPurch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { LogPurch } & 17 & 2.73 & 0.121 & 0.101 & ( 2.7,2.8 ) \\\hline\end{array}\end{array}$$
-Choose the statement that explains which confidence interval more precisely depicts the data and why.

• A) The confidence interval for the untransformed data is more precise because the values are in actual dollars which is more meaningful.
• B) The confidence interval for the geometric mean is more precise because the distribution of the
• Log-transformed data is more symmetric.
• 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:

1960s

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Major Cases

Significant legal decisions or landmark judgments that have had a profound impact on law and society.

Supreme Court

The highest federal court in a country, typically having the ultimate authority in interpreting the constitution and laws.

Sherman Act

The federal antitrust law enacted in 1890 that prohibited monopolization and conspiracies to restrain trade.