Which Supermarket Has the Lowest Prices in Town? All Claim

Short Answer

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: $$\begin{array} { l l r } \bar { x } \mathrm {~A} = 2.09 & \bar { x } \mathrm {~B} = 1.99 & \bar { d } = .10 \\\mathrm {~s} _ { \mathrm { A } } = 0.22 & { } ^ { s } \mathrm {~B} = 0.19 & s _ { d } = .03\end{array}$$
Assuming the data represent a matched pairs design, calculate the confidence interval for comparing mean prices using a $95 \%$ confidence level.
A) . $10 \pm .00588$
B) $10 \pm .056975$
C). $10 \pm .1255$
D) $.10 \pm .004935$