Question

To test for any significant difference in the mean number of hours between breakdowns for four machines, the following data were obtained.

Machine 1	Machine 2		Machine 3		Machine 4
6.4	8.7		11.1		9.9
7.8	7.4		10.3		12.8
5.3	9.4		9.7		12.1
7.4	10.1		10.3		10.8
8.4	9.2		9.2		11.3
7.3	9.8		8.8		11.5

The mean times between breakdowns are 7.1, 9.1, 9.9 and 11.4 hours respectively. In the analysis of variance, MSTR = 19.26 and MSE = .97. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment error rate of .05 is desired.

There are six pairwise comparisons among the 4 machines. What error rate should be used for each pairwise comparison (to 4 decimals)?

Using t = 2.845 for the above error rate, calculate the Bonferroni LSD value (to 2 decimals).


Complete the table below to determine whether there are any significant differences between population means.

Difference	Absolute Value	Conclusion
x1 - x2		SelectSignificant differenceNo significant differenceItem 4
x 1 - x3		Significant difference or No significant difference
x1 - x4		Significant difference or No significant difference
x2 - x3		Significant difference or No significant difference
x2 - x 4		Significant difference or No significant difference
x3 - x4		Significant difference or No significant difference

Answer 1

error rate should be used for each pairwise comparison = 0.05/6 = 0.0083

Bonferroni LSD critical value=t*√(MSE(1/ni+1/nj)) = 1.62

if absolute difference of means > LSD,means are significnantly different ,otherwise not

	mean difference	absolute mean difference		LSD					result
µ1-µ2	-2.00	2.00		1.62					means are different
µ1-µ3	-2.80	2.80		1.62					means are different
µ1-µ4	-4.30	4.30		1.62					means are different
µ2-µ3	-0.80	0.80		1.62					means are not different
µ2-µ4	-2.30	2.30		1.62					means are different
µ3-µ4	-1.50	1.50		1.62					means are not different