Question

A one-way analysis of variance experiment produced the following ANOVA table. (You may find it useful to reference the q table).

SUMMARY
Groups	Count				Average
Column 1	6				0.72
Column 2	6				1.74
Column 3	6				2.51
Source of Variation	SS		df	MS	F	p-value
Between Groups	8.50		2	4.25	16.35	0.0002
Within Groups	3.93		15	0.26
Total	12.43		17

b. Calculate 99% confidence interval estimates of μ₁ − μ_2,μ₁ − μ_3, and μ₂ − μ₃ with Tukey’s HSD approach. (If the exact value for n_T – c is not found in the table, then round down. Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

Population Mean Differences	Confidence Interval
μ1 − μ2	[		,		]
μ1 − μ3	[		,		]
μ2 − μ3	[		,		]

Answer 1

Critical value for , df=15 and k=3 is

And

The Tukey's HSD will be

Following table shows the confidence intervals

The required confidence intervals are:

groups (i-j)	Lower limit	Upper limit
mu1-mu2	-2.03	-0.01
mu1-mu3	-2.8	-0.78
mu2-mu3	-1.78	0.24