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:

Endergonic Reactions

Chemical reactions that require an input of energy to proceed and are characterized by a positive change in free energy.

Transition State

A high-energy state during a chemical reaction where reactants are converted into products, representing the point of maximum energy during the reaction.

Substrates

A substance or layer that underlies something, or on which some process occurs, in various scientific fields, it often refers to the base on which an organism grows or the substance enzymes act upon.

Cofactor

A coenzyme or metal ion that associates with an enzyme and is necessary for its function.