Question

Consider the data in the table collected from three independent populations. Sample 1 Sample 2 Sample 3 a) Calculate the total sum of squares (SST) and partition the SST into its two components, the sum of squares between (SSB) and the sum of squares within (SS) b) Use these values to construct a one-way ANOVA table c) using α-0.05, what conclusions can be made concerning the population means? 14 Click the lcon to view a table of critical F-scores for a 0.05.

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
sample 1	3	18	6	7
sample 2	3	12	4	7
sample 3	4	20	5	36.66667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	6	2	3	0.152174	0.861605	4.737414
Within Groups	138	7	19.71429
Total	144	9

So from the above output

vomhe above o Ssw 13 8 0.IS2 138 19 14 Talo

( c ) at alpha = 0.05 l.o.s f critical value = 4.737

Decision :

F CAL < F CRITICAL

i.e ., 0.152 < 4.737

so fail to reject H0

the population means are equal ( same )