Analysis of variance may be used in an industrial setting. For example, man- agers of a soda-bottling company suspected that four filling machines were not filling the soda cans in a uniform way. An experiment on four machines doing five runs each gave the data in the following table.
Liquid Weight of Machine-Filled Cans in Ounces
|
Machine A
|
Machine B
|
Machine C
|
Machine D
|
|
12.05
|
11.98
|
12.04
|
12.00
|
|
12.07
|
12.05
|
12.03
|
11.97
|
|
12.04
|
12.06
|
12.03
|
11.98
|
|
12.04
|
12.02
|
12.00
|
11.99
|
|
11.99
|
11.99
|
11.96
|
11.96
|
Based on the analysis of variance, is there a difference in the average number of ounces filled by the four machines? Apply Tukey's HSD test to compare the mean differences if the overall ANOVA test is significant at the 5% level.