Which Supermarket Has the Lowest Prices in Town? All Claim

question 77

Multiple Choice

Which supermarket has the lowest prices in town? All claim to be cheaper, but an independent agency recently was asked to investigate this question. The agency randomly selected 100 items common to each of two supermarkets (labeled A and B) and recorded the prices charged by each supermarket. The summary results are provided below:
$$\begin{array} { l l r } \bar { x } \mathrm {~A} = 2.09 & \bar { x } \mathrm {~B} = 1.99 & \bar { d } = .10 \\s _ { \mathrm { A } } = 0.22 & \mathrm {~s} _ { \mathrm { B } } = 0.19 & s _ { d } = .03\end{array}$$
Assuming a matched pairs design, which of the following assumptions is necessary for a confidence interval for the mean difference to be valid?

• A) None of these assumptions are necessary.
• B) The samples are randomly and independently selected.
• C) The population variances must be equal.
• D) The population of paired differences has an approximate normal distribution.

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Definitions:

Sensitivity Coefficients

Numbers that measure how much a dependent variable changes when an independent variable changes by one unit, often used in financial models to gauge risk.

Single-Index Structure

A model used in finance to describe the performance of assets in relation to a single market index, capturing the proportion of an asset's risk and return that can be explained by the market index.

Expected Returns

The anticipated return on an investment based on historical data or probability-weighted scenarios.

Sensitivity Coefficients

Measures in sensitivity analysis that quantify how the output of a model changes in response to changes in input variables.