The Tastee Bakery Company supplies a bakery product to many supermarkets in a me
ID: 3303232 • Letter: T
Question
The Tastee Bakery Company supplies a bakery product to many supermarkets in a metropolitan area. The company wishes to study the effect of the shelf display height employed by the supermarkets on monthly sales (measured in cases of 10 units each) for this product. Shelf display height, the factor to be studied, has three levels – bottom (B), middle (M), and top (T) – which are the treatments. To compare these treatments the bakery uses a completely randomized experimental design. The following figure gives the output of a One-way ANOVA. Using the computer output:
A) Test the null hypothesis that all population means Mm, Mb, and Mt of the three levels are equal by setting the significance level equals to 5%. On the basis of this test, can we conclude that the bottom, middle, and top shelf display heights have different effects on mean monthly sales? (State all hypothesis testing steps.)
B) Consider the pairwise differences Mm - Mb, Mt - Mb, and Mt - Mm.. Find estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the meaning of each interval in practical terms. Which display height maximizes mean sales?
One way ANOVA: Bakery Sale versus Display Height
Source DF SS MS F P
Display Height 2 2273.88 1136.94 184.57 0.000
Error 15 92.40 6.16
Total 17 2366.2
Tukey 95% simultaneous Confidence Intervals
Bottom subtracted from:
Lower Center Upper
Middle 17.681 21.400 25.119
Top -8.019 -4.300 -0.581
Middle subtracted from:
Lower Center Upper
Top -29.419 -25.700 -21.981
Individual 95% Confidence Intervals for mean based on pooled StDev
Level N Mean StDev
Bottom 6 55.800 2.477 Pooled Stdev = 2.482 56 64 72 80
MIddle 6 77.200 3.103
Top 6 51.500 1.648
Explanation / Answer
a) as p value is significantly low we reject null hypothesis.
we have sufficient evidence to conclude that the bottom, middle, and top shelf display heights have different effects on mean monthly sales
b)
from above estimate of Mm - Mb =21.4
and 95% confidence interval =17.681 ; 25.119
estimate of Mt - Mb =-4.3
and 95% confidence interval =-8.019 ; -0.581
estimate of Mt - Mm =-25.7
and 95% confidence interval =-29.419 ; -21.981
above intervals gives 95% confidence to contian true difference between two poulation mean.
from here we can see that middle height maximizes mean sales
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