We Are Interested in Comparing the Average Supermarket Prices of Two

question 67

Multiple Choice

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.

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Definitions:

Modified AGI

Adjusted Gross Income (AGI) altered by adding back certain deductions, often used to determine eligibility for specific tax benefits.

Joint Tax Return

A tax filing status for married couples who choose to file one tax return jointly, combining their incomes and deductions.

Qualifying Child

A dependent who meets specific IRS criteria regarding relationship, age, residence, and support, allowing taxpayers to claim certain credits and deductions.

Education Tax Credits

Tax credits that taxpayers can claim for eligible educational expenses, aimed at reducing the amount of tax owed to the government.