Question

The following data are given for a two-factor ANOVA with two treatments and three blocks.

Block 1 2

A 47 30

B 31 29

C 47 36

Using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.

State the decision rule for treatments. (Round your answer to 1 decimal place.)

State the null and alternate hypotheses for blocks. (Round your answer to 1 decimal place.)

Also, state the decision rule for blocks.

Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round your SS, MS values to 3 decimal places and F value to 2 decimal places.)

Answer 1

using excel>data> data analysis> Two way ANOVA

we have

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
A	2	77	38.5	144.5
B	2	60	30	2
C	2	83	41.5	60.5
1	3	125	41.66667	85.33333
2	3	95	31.66667	14.33333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
treatment	142.3333	2	71.16667	2.497076	0.285953	19
Block	150	1	150	5.263158	0.148743	18.51282
Error	57	2	28.5
Total	349.3333	5

the decision rule for treatment: we will reject HO if F >19.0

the null and alternate hypotheses for blocks is

Ho:all the means of block are same.

Ha : at least two mean differs significantly

the decision rule for blocks : reject Ho if F> 18.5

SST = 142.333, SSB =150 , SS total =349.33, and SSE = 57

an ANOVA table.

ANOVA
Source of Variation	SS	df	MS	F	P-value
treatment	142.333	2	71.167	2.50	0.285953
Block	150	1	150	5.26	0.148743
Error	57	2	28.5
Total	349.333	5

since p-value for treatment and blocks are greater than so we conclude that means are same for block and treatments