Question

Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level. Treatment 1 - 8, 11 and 10. Treatment 2 - 3, 2, 1, 3, and 2. Treatment 3 - 3, 4, 5 and 4. - (a) Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.) (b) Complete an ANOVA table. (Round your answers to 2 decimal places.) Source SS df MS F Treatments Error Total

Answer 1

The summary statistics obtained from the given data are as below.

	Treatment 1	Treatment 2	Treatment 3
Total	29	11	16
n	3	5	4
Mean	9.67	2.20	4.00
Sum Of Squares	4.67	2.80	2.00
Variance	2.3334	0.7	0.6667

The Hypothesis:

H0: There is no difference between the means of the three treatments

Ha: The mean of at least one treatment is different from the others.

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(a) Overall Mean = (29 + 11 + 16) / 12 = 56/12 = 4.67

SS treatment = SUM [n* ( Individual Mean - overall mean)²] = 3 * (9.67 - 4.67)² + 5 * (2.2 - 4.67)² + 4 * (4 - 4.67)² = 107.210

SS error = SUM (Sum of Squares) = 4.67 + 2.8 + 2.2 = 9.47

SS Total = SS Treatments + SS error = 107.21 + 9.47 = 116.68

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The ANOVA table is as below.

Source	SS	DF	Mean Square	F
Treatments	107.210	2	53.605	50.96
Within/Error	9.467	9	1.052
Total	116.68	11

df treatment = k - 1 = 3 - 1 = 2

MS Treatment = SS Treatment / df Treatment = 107.21 / 2 = 53.61

df error = N - k = 12 - 3 = 9

MS error = SS error / df error = 9.47 / 12 = 1.05

F = MS Treatment / MS Error = 53.61 / 1.05 = 50.96

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