The Tastee Bakery Company supplies a bakery product to many supermarkets in a metropolitan area. The company wishes to study the effect of shelf display height employed by the supermarkets on monthly sales (measured in 10 unit cases). Shelf display height, the factor to be studied, has three levels - bottom (B), middle (M), and top (T) - which are the measurements. Let µ_{B}, µ_{M, }and u_{T} represent the mean monthly sales when using the bottom, middle and top shelf display heights.
a) Perform a one-way ANOVA.
b) Test the null hypothesis that the mean monthly sales are equal by setting α = 0.05. On the basis of this, can we conclude that the bottom, middle and top shelf display heights have different effects on mean monthly sales?
Shelf Display Height
Bottom (B) Middle (M) Top (T)
58.2 73.0 52.4
53.7 78.1 49.7
55.8 75.4 50.9
55.7 76.2 54.0
52.5 78.4 52.1
58.9 82.1 49.9