Question

# Sales of a product may depend on its placement in a store. Candy manufacturers frequently offer discounts to retailers who display their products more prominently than competing brands. To examine this phenomenon more carefully, a candy manufacturer (with the assistance of a national chain of restaurants) planned the following experiment. In 20 restaurants, the manufacturer’s brand was displayed behind the cashier’s counter with all the other brands (this was called position 1). In another 20 restaurants, the brand was placed separately but close to the other brands (position 2). In a third group of 20 restaurants, the candy was placed in a special display next to the cash register (position 3). The number of packages sold during 1week at each restaurant was recorded. Is there sufficient evidence to infer that sales of candy differ according to placement?

Solution

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We should use a one-way ANOVA because there is only one factor in this study: Post. The one-way ANOVA can tell us if there is a difference in the candy sales between the three groups. It is a hypothesis testing procedure, so the hypotheses we wish to test are:

$H_{0}: \text{There is no difference in the average candy sales for the three groups.}$

$\mu_1=\mu_2=\mu_3$

$H_{1}: \text{There is a difference in the average candy sales for the three groups.}$

To make a decision about the null hypothesis, we need to compare the $p$-value to the significance level $\alpha$.