Given a recent outbreak of illness caused by E. coli bacteria, the mayor in a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant's cleanliness. In order to investigate this possibility, the mayor has five restaurant inspectors grade (scale of 0 to 100) the cleanliness of three restaurants. The results are shown in the accompanying table.

..................................Restaurant

Inspector................1............2............3

1........................72..........54...........84

2........................68..........55...........85

3........................73..........59...........80

4........................69..........60...........82

5........................75..........56...........84

a. Use Excel to generate the appropriate ANOVA table at the 5% significance level.

b. At the 5% significance level, can you conclude that the average grades differ by restaurant?

c. If the average grades differ by restaurant, use Tukey's HSD method at the 5% significance level to determine which averages differ.

d. At the 5% significance level, can you conclude that the average grades differ by inspector? Does the mayor have cause for concern?