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	3				0.66
Column 2	3				1.24
Column 3	3				2.85
Source of Variation	SS		df	MS	F	p-value
Between Groups	8.02		2	4.01	4.09	0.0758
Within Groups	5.86		6	0.98
Total	13.88		8

a. Conduct an ANOVA test at the 5% significance level to determine if some population means differ.

• Do not reject H₀; we cannot conclude that some population means differ.

• Reject H₀; we cannot conclude that some population means differ.

• Do not reject H₀; we can conclude that some population means differ.

• Reject H₀; we can conclude that some population means differ.

b. Calculate 95% 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.)

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

Answer 1

a)since p value >0.05

Do not reject H₀; we cannot conclude that some population means differ.

b)

MSE=			0.9800
df(error)=			6
number of treatments =			3
pooled standard deviation=Sp =√MSE=			0.990

critical q with 0.05 level and k=3, N-k=6 df=			4.34
Tukey's (HSD) =(q/√2)*(sp*√(1/ni+1/nj)         =			2.48

			Lower bound	Upper bound	differ
			(xi-xj)-ME	(xi-xj)+ME
μ1-μ2			-3.06	1.90	not significant difference
μ1-μ3			-4.67	0.29	not significant difference
μ2-μ3			-4.09	0.87	not significant difference

c)

none of the means differ significantly