Question

μ1, μ2, and μ3 are the means of normal distributions with an equal but unknown variance. Our goal is to test H0: μ1 = μ2 = μ3 vs Ha: at least two μj are different, by taking random samples of size 4 from each distributions. Let x1 = 28, x2 = 46, x3 = 34, and ??x2ij =1038

(a) Construct an ANOVA table.
(b) Carry out the 5% significance level test.

(c) What is the HSD in this problem?

Answer 1

(a)

	x	n	n*(x - xgrand)²
Group 1	28	4	256
Group 2	46	4	400
Group 3	34	4	16
xgrand	36
			Sum
			672
Source	SS	df	MS	F	p-value
Between	672	2	336	8.262295	0.009179
Error	366	9	40.66667
Total	1038	11

(b) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

The p-value is 0.009179.

Since the p-value (0.009179) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that not all means are equal.

(c) HSD = 2.26*40.66667/4 = 7.21