Question

Given the following information obtained from four normally distributed populations, construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS" to 2 decimal places, "MS" to 4 decimal places, and "F" to 3 decimal places.) SST = 76.83; SSTR = 11.41; c = 4; n1 = n2 = n3 = n4 = 15

ANOVA
Source of Variation	SS	df	MS	F	p-value
Between Groups					0.028
Within Groups
Total

At the 5% significance level, what is the conclusion to the ANOVA test of mean differences?

Reject H₀; we can conclude that some means differ.

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

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

Reject H₀; we cannot conclude that some means differ.

Answer 1

Here we have SST = 76.83 , SSTR = 11.41

So, SSE = SST - SSTR = 76.83 - 11.41 = 65.42

between groups df = c -1 = 4-1 =3

N = n1 + n2 + n3 + n4 = 15 + 15 + 15 + 15 = 60

Total df = N-1 = 60 -1 = 59

Within group df = 59 - 3 = 56

Mean sum of squares are given by

Test statistic :

ANOVA

Source of Variation	SS	df	MS	F	P - value
Between Groups	11.41	3	3.8033	3.256	0.028
Within Groups	65.42	56	1.1682
Total	76.83	59

Here p value < ( 0.05 )

Hence we reject null hypothesis.

Reject H0; we can conclude that some means differ.