Question

# Let µ1, µ2, and µ3 be the means of normal distributions with a common but unknown...

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?

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

Ha: 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

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