Which Supermarket Has the Lowest Prices in Town? All Claim

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 population of paired differences has an approximate normal distribution.
C) The population variances must be equal.
D) The samples are randomly and independently selected.