We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table:
$$\begin{array}{l}
\begin{array} { c | c c | c }
&\text { Price }\
\text { Supermarket } & \text { Brand 1 } & \text { Brand 2 } & \text { Difference } \
\hline 1 & \$ 2.25 & \$ 2.30 & \$ - 0.05 \
2 & 2.47 & 2.45 & 0.02 \
3 & 2.38 & 2.44 & - 0.06 \
4 & 2.27 & 2.29 & - 0.02 \
5 & 2.15 & 2.25 & - 0.10 \
6 & 2.25 & 2.25 & 0.00 \
7 & 2.36 & 2.42 & - 0.06 \
8 & 2.37 & 2.40 & - 0.03 \
\hline & \mathrm { x } _ { 1 } = 2.3125 & \mathrm { x } _ { 2 } = 2.3500 & \mathrm {~d} = - 0.0375 \
& \mathrm {~s} _ { 1 } = 0.1007 & \mathrm {~s} _ { 2 } = 0.0859 & \mathrm {~s} _ { \mathrm { d } } = 0.0381
\end{array}
\end{array}$$ If the problem above represented a paired difference, what assumptions are needed for a confidence interval for the mean difference to be valid?
A) The population variances are equal.
B) The population of paired differences has an approximately normal distribution.
C) The samples were independently selected from each population.
D) All of the above are needed.

Question

We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table: 
$$\begin{array}{l}
\begin{array} { c | c c | c } 
&\text { Price }\
\text { Supermarket } & \text { Brand 1 } & \text { Brand 2 } & \text { Difference } \
\hline 1 & \$ 2.25 & \$ 2.30 & \$ - 0.05 \
2 & 2.47 & 2.45 & 0.02 \
3 & 2.38 & 2.44 & - 0.06 \
4 & 2.27 & 2.29 & - 0.02 \
5 & 2.15 & 2.25 & - 0.10 \
6 & 2.25 & 2.25 & 0.00 \
7 & 2.36 & 2.42 & - 0.06 \
8 & 2.37 & 2.40 & - 0.03 \
\hline & \mathrm { x } _ { 1 } = 2.3125 & \mathrm { x } _ { 2 } = 2.3500 & \mathrm {~d} = - 0.0375 \
& \mathrm {~s} _ { 1 } = 0.1007 & \mathrm {~s} _ { 2 } = 0.0859 & \mathrm {~s} _ { \mathrm { d } } = 0.0381
\end{array}
\end{array}$$ If the problem above represented a paired difference, what assumptions are needed for a confidence interval for the mean difference to be valid?
A) The population variances are equal.
B) The population of paired differences has an approximately normal distribution.
C) The samples were independently selected from each population.
D) All of the above are needed.

Quizplus · Accepted Answer

The Answer of We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table: 
$$\begin{array}{l}
\begin{array} { c | c c | c } 
&\text { Price }\
\text { Supermarket } & \text { Brand 1 } & \text { Brand 2 } & \text { Difference } \
\hline 1 & \$ 2.25 & \$ 2.30 & \$ - 0.05 \
2 & 2.47 & 2.45 & 0.02 \
3 & 2.38 & 2.44 & - 0.06 \
4 & 2.27 & 2.29 & - 0.02 \
5 & 2.15 & 2.25 & - 0.10 \
6 & 2.25 & 2.25 & 0.00 \
7 & 2.36 & 2.42 & - 0.06 \
8 & 2.37 & 2.40 & - 0.03 \
\hline & \mathrm { x } _ { 1 } = 2.3125 & \mathrm { x } _ { 2 } = 2.3500 & \mathrm {~d} = - 0.0375 \
& \mathrm {~s} _ { 1 } = 0.1007 & \mathrm {~s} _ { 2 } = 0.0859 & \mathrm {~s} _ { \mathrm { d } } = 0.0381
\end{array}
\end{array}$$ If the problem above represented a paired difference, what assumptions are needed for a confidence interval for the mean difference to be valid?
A) The population variances are equal.
B) The population of paired differences has an approximately normal distribution.
C) The samples were independently selected from each population.
D) All of the above are needed.

We Are Interested in Comparing the Average Supermarket Prices of Two