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 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). $10 \pm .004935$
C). $10 \pm .1255$
D). $10 \pm .056975$

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:
$$\begin{array} { l l r } 
\bar { x } \mathrm {~A} = 2.09 & \bar { x } \mathrm {~B} = 1.99 & \bar { d } = .10 \
s _ { \mathrm { A } } = 0.22 & \mathrm {~s} \mathrm {~B} = 0.19 & s d = .03
\end{array}$$
Assuming 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). $10 \pm .004935$
C). $10 \pm .1255$
D). $10 \pm .056975$

Quizplus · Accepted Answer

The correct answer is A because the confidence interval for comparing mean prices using a 95% confidence level is 10 ± .00588. This is calculated using the formula:CI = (x̄A - x̄B) ± t* (s_d) * √(1/nA + 1/nB)where:x̄A = mean price of supermarket Ax̄B = mean price of supermarket Bs_d = standard deviation of the difference between the pricesnA = number of items in sample AnB = number of items in sample Bt* = t-value for the desired confidence levelPlugging in the values from the question, we get:CI = (2.09 - 1.99) ± 1.96* (0.03) * √(1/100 + 1/100)CI = 0.10 ± 0.00588CI = 10 ± .00588

Which Supermarket Has the Lowest Prices in Town? All Claim