Question

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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	3				0.67
Column 2	3				1.87
Column 3	3				2.31
Source of Variation	SS		df	MS	F	p-value
Between Groups	9.68		2	4.84	8.49	0.0178
Within Groups	3.43		6	0.57
Total	13.11		8

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	[		,		]

c. Given your response to part b, which means significantly differ?

Population Mean Differences	Can we conclude that the population means differ?
μ1 − μ2
μ1 − μ3
μ2 − μ3

Answer 1

b) and c)

count, ni =	3	3	3
mean , x̅ i =	0.67	1.87	2.31

Level of significance	0.01
no. of treatments,k	3
DF error =N-k=	6
MSE	0.57
q-statistic value(α,k,N-k)	6.33

critical value = q*√(MSE/2*(1/ni+1/nj)) =2.7592

confidence interval = mean difference ± critical value

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	-1.200	2.7592	-3.96	1.56	means are not different
µ1-µ3	-1.640	2.7592	-4.40	1.12	means are not different
µ2-µ3	-0.440	2.7592	-3.20	2.32	means are not different

if confidence interval contans zero, then means are not different.
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