A Local Consumer Reporter Wants to Compare the Average Costs

question 36

Multiple Choice

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket.
The results of the ANOVA are summarized in the following table. $$\begin{array} { l r r r r r } \text { Source } & \text { df } & \text { Anova SS } & \text { Mean Square } & \text { F Value } & \text { Pr > F } \\\hline \text { Supermkt } & 2 & 2.6412678 & 1.3206399 & 39.23 & 0.0001 \\\text { Item } & 59 & 215.5949311 & 3.6541514 & 108.54 & 0.0001 \\\text { Error } & 118 & 3.9725322 & 0.0336655 & &\end{array}$$ Based on the p-value of the test, make the proper conclusion.

• A) There is sufficient evidence (at \(\alpha = .01\) ) to indicate that the mean prices of grocery items at the three supermarkets are identical.
• B) There is insufficient evidence (at \(\alpha = .01\) ) to indicate differences among the mean prices of grocery items at the three supermarkets.
• C) There is sufficient evidence (at \(\alpha = .01\) ) to indicate differences among the mean prices of grocery items at the three supermarkets.
• D) No conclusions can be drawn from the given information.

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Definitions:

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The price at which the quantity demanded by consumers equals the quantity supplied by producers, leading to market equilibrium.