Supermarkets often place similar types of cereal on the same supermarket shelf. The shelf placement for 77 cereals was recorded as well their sugar content. Does sugar content vary by shelf? Here€™s a boxplot and an ANOVA table.

a) What kind of design or study is this?
b) What are the null and alternative hypotheses?
c) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of sugar content and shelf placement.)

d) Can we conclude that cereals on shelf 2 have a different mean sugar content than cereals on shelf 3? Can we conclude that cereals on shelf 2 have a different mean sugar content than cereals on shelf 1? What can we conclude?
e) To check for significant differences between the shelf means, we can use a Bonferroni test, whose results are shown at the top of the next column. 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 d?

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15 10H Shelf Sum of Mean Source DF Squares Square F-ratio P-value Shelf 2 248.4079 124.204 7.3345 0.0012 Error 74 1253.1246 16.934 Tota 76 1501.5325 Leve n Mean StdDev 1 20 4.80000 4.57223 2 21 9.61905 4.12888 3 36 6.52778 3.83582 Dependent Variable: SUGARS Bonferroni Mean Differ (I) J) ence SHELF SHELF (IJ Error value 95% Confidence Interval Std P- Lower Upper Bound Bound -4.819 1.2857 0.001 7.969 1.670 -1.728 1.1476 0.4094.539 1.084 4.819 1.2857 D.00 1.670 7.969 3.091 1.1299 0.023 0.323 5.859 1.728 1.1476 0.4091.084 4.539 -3.091 1.1299 0.0235.859 0.323