We first saw data on breakfast cereals in Chapter 7. Supermarkets often place similar types of cereal on the same supermarket shelf. We have data on the shelf as well as the sugar, sodium, and calorie content of 77 cereals. Does sugar content vary by shelf? At the top of the next column is a box plot and an ANOVA table for the 77 cereals.

a) What are the null and alternative hypotheses?
b) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of Sugars and Shelves.)
c) Can we conclude that cereals on shelf 2 have higher mean sugar content than cereals on shelf 3? Can we conclude that cereals on shelf 2 have higher mean sugar content than cereals on shelf 1? What can we conclude?
d) To check for significant differences between the shelf means, we can use a Bonferroni test, whose results are shown below. For each pair of shelves, the difference is shown along with its standard error and significance level. What does it say about the questions in part c?
Dependent Variable: SUGARS

3 5050 (6) siebng Sum of Mean Source DF Squares Square F-Ratio P-Value Shelf 2 244.20 122.10 7.2721 0.0013 Error 74 1242.47 Total76 1486.68 Means and Std Deviations Level Mean StdDev 0 20 4.8500 4.51051 21 9.61905 4.12888 36 6.52778 3.83582 Dependent Variable: SUGARS Mean 95% Confidence (I) ) Difference Std. SHELF SHELF (I-) Error P-Value Interval Bonferroni Lower Upper Bound Bound 1 2-4.769) 1.3524 0.0033-8.155 -1.383 31.678 1.1941 0.5070-4.6831.328 2 1 4.769() 1.3524 0.0033 1.383 8.155 3 3.091 11048 0.0237 0.329 5.853 3 1 .678 1.1941 0.50701.328 4.483 2 3.091) 11048 0.0237-5.853 -0.329 The mean difference is significant at the 0.05 level.