Question

Consider the partially completed​ one-way ANOVA summary table below.

Source	Sum of Squares	Degrees of Freedom	Mean Sum of Squares	F
Between	35	5	7	1.167
Within	144	24	6
Total	179	29

c. Using alpha = 0.05, what conclusions can be made concerning the population​ means?

Answer 1

Solution:

= 0.05

d.f._numerator = df(between) = 5

d.f._denominator = df(within) = 24

Use F table to find the critical value .

= F_0.05,5,24 = 2.62

Now , test statistic F= 1.167

1.167 < 2.62

i.e.. test statistic < critical F value

Fail to reject H₀ : all means are equal

So , there is not sufficient evidence to reject that the means of given 6 groups are same.

i.e. not sufficient evidence to support that one or more pairs from given 6 means are different.