Question

Let µ1, µ2, and µ3 be the means of normal distributions with a common but unknown variance. We want to test H0 : µ1 = µ2 = µ3 against Ha : at least two µj are different, by taking random samples of size 4 from each distributions. Let PP x1· = 28, x2· = 46, x3· = 34, and x 2 ij = 1038.

(a) Construct an ANOVA table. (b) Carry out the 5% significance level test. (c) What is the HSD in this problem?

Answer 1

From the given data,

a)

	X	n	n*(x - xgrand)²
Group1	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)

Hypothesis :

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