Analysis of variance may be used in an industrial setting. For example, managers 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.

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.

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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