Question

In: Statistics and Probability

A fast food chain plans to add a new item to its menu. There are three...

A fast food chain plans to add a new item to its menu. There are three possible campaigns for the new menu item. They introduced the product at locations in several randomly selected markets. A different promotion was used at each location, and the weekly sales of the new item are recorded for the first four weeks. Management is interested in determining the differences in the promotion campaigns with regard to total sales. In addition, it wants to know if the age of the location of the restaurant influences the promotion.

What kind of Stats test should be done?(ANOVA,MANOVA ..etc) State Hypotheses and Assumptions

Solutions

Expert Solution

For the given scenario, we need to use the two-way analysis of variance or two way ANOVA F test for checking the given claims. A management of the fast food chain should use two way ANOVA for checking their claims regarding the total sales. The null and alternative hypotheses for this two way ANOVA are given as below:

Hypothesis 1

Null hypothesis: H0: There is no significant difference in the average sales for the new menu item for three different campaigns.

Alternative hypothesis: Ha: There is a significant difference in the average sales for the new menu item for three different campaigns.

Hypothesis 2

Null hypothesis: H0: There is no significant difference in the average sales for the new menu at different restaurants with different age of the locations.

Alternative hypothesis: Ha: There is a significant difference in the average sales for the new menu at different restaurants with different age of the locations.

Hypothesis 3

Null hypothesis: H0: There is no statistically significant interaction between the different campaigns and age of the location of restaurants.

Alternative hypothesis: Ha: There is a statistically significant interaction between the different campaigns and age of the location of restaurants.

The assumptions for this two way ANOVA are given as below:

There is one independent variable such as a sale of the new menu item and two independent variables such as campaign and age of restaurant.

We assume that the samples for sales of new menu items are taken from normally distributed populations.

Also, we assume that the variances for the different groups are approximately equal.

orchestra answered 2 years ago
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