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

Question

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

Quizplus · Accepted Answer

The confidence interval for the mean difference in a matched pairs design is calculated as $\bar{d} \pm t^* \frac{s_d}{\sqrt{n}}$. With $\bar{d} = 0.10$, $s_d = 0.03$, $n = 100$, and using a t-distribution with 99 degrees of freedom, the interval is approximately $0.10 \pm 0.00588$.

Which Supermarket Has the Lowest Prices in Town? All Claim