The following data were collected for a randomized block analysis of variance design with four populations and eight blocks:

Group 1 Group 2 Group 3 Group 4 Block 1 56 44 57 84 Block 2 34 30 38 50 Block 3 50 41 48 52 Block 4 19 17 21 30 Block 5 33 30 35 38 Block 6 74 72 78 79 Block 7 33 24 27 33 Block 8 56 44 56 71

a. State the appropriate null and alternative hypotheses for the treatments and determine whether blocking is necessary.

b. Construct the appropriate ANOVA table.

c. Using a significance level equal to 0.05, can you conclude that blocking was necessary in this case?
Use a test-statistic approach.

d. Based on the data and a significance level equal to 0.05, is there a difference in population means for the four groups? Use a p-value approach.

e. If you found that a difference exists in part

d, use the LSD approach to determine which populations have different means.