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Do grocery stores shelve breakfast cereals (Frosted Flakes, etc.) aimed at children on the third (bottom) shelf and healthier cereals on higher shelves? We have a data set that tells us the sugar content of breakfast cereals and the shelf on which they are located. Shelf 3 is the lowest shelf, 2 is in the middle, and 1 is on the top. We ran an ANOVA with sugar in grams as the response variable and shelf as the factor. This is what we got (higher numbers mean higher sugar content):
One-way ANOVA: Sugars versus Shelf
Source DF SS MS F P
Shelf 2 220.2 110.1 6.60 0.002
Error 73 1217.7 16.7
Total 75 1437.9
S = 4.084 R-Sq = 15.32% R-Sq(adj) = 13.00%
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev
1 19 5.105 4.483
2 21 9.619 4.129
3 36 6.528 3.836
Pooled StDev = 4.084
To test our initial hypothesis that cereal shelved on the bottom shelf is the most sugary, we could test the contrast:
H0: u = u3 - ½(u1 + u2) = 0
Against the alternative:
HA: u = u3 - ½(u1 + u2) > 0
That is, our alternative is that Shelf 3 cereals have a higher sugar content than the average of shelves 1 and 2.
Using three decimal places, the sample value of the contrast is__________?
The standard error of the contrast is 1.092. Should
