Question

Analysis of Variance Mean Std.Dev. Sample Size General Mills 1.469 1.248 13 Kellogg’s 1.764 2.349 11 Quaker 2.567 2.174 6 TOTAL 1.797 1.880 30 The dataset Cereal shows the number of grams of fiber per serving for 30 different breakfast cereals from three different companies. The summary statistics are shown below. Conduct an analysis of variance test to determine whether there is a difference in mean number of grams of fiber per cereal between the three companies.

1. Check to see if the conditions for ANOVA are met. Show your R code and output. Interpret your results in the context of this problem, using complete sentence(s). 2. State the hypotheses for this ANOVA. 3. Perform the ANOVA. Show your R code and output. a. Interpret the results of your ANOVA table in the context of this problem, using complete sentence(s). b. Interpret the results of your two-way comparisons in the context of this problem, using complete sentence(s). 4. Comment on the power of this test. What could be done to improve the power? What other limitations, if any, do you note in this test?

Answer 1

Mean	St.Dev	Sample Size
General Mills	1.469	1.248	13
Kellogg's	1.764	2.349	11
Quaker	2.567	2.174	6
TOTAL	1.797	1.880	30

we have to test that here is a difference in mean number of grams of fiber per cereal between the three companies

Ha: at least one mean is different

since

                                           

since as for whole data standard deviation is given 1.880

so

so

                                   =106.032

and ERRor sum of square is givenn by

                                                   

                                                    

=5.1758

so error sum of square = Total SS - treatment SS

                                =106.032 - 5.1758

                                 =100.8562

                                            

source	SS	df	MS	F
between companies	5.1758	2	2.59	0.692
within companies	100.8562	27	3.74
total		29

                                                 at 0.05 level F value =3.35

since F calculated < F tabulated

so there is no significance difference between companies means.