We also have data on the protein content on the 77 cereals in Exercise 45. Does protein 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 protein content and shelf placement.)

d) Can we conclude that cereals on shelf 2 have a lower mean protein content than cereals on shelf 3? Can we conclude that cereals on shelf 2 have a lower mean protein 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 here. 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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2 4 2 3 Shelf Sum of Mean Source DF Squares SqueF-ratio P-value Shelf 2 12.4258 6.2129 5.8445 0.0044 Error 74 78.6650 1.0630 Tota 76 91.0909 Level n Mean 20 2.65000 1.46089 21 1.90476 0.99523 36 2.86111 0.72320 Dependent Variable: PROTEIN Bonferroni Mean Differ 95% Confidence (I) (J) ence Std. P SHELF SHELF (IJ Error value Interval Lower Upper Bound Bound 0.75 0.322 0.070 0.04 1.53 -0.21 0.288 1.000-0.92 0.49 0.75 0.322 0.0701.53 0.04 -0.96 0.283 0.0041.65-0.26 0.2 0.288 1.000 0.49 0.92 0.96 0.283 0.004 0.26 1.65