Question

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

  

	Treatment
Block	1	2
A	43	31
B	33	22
C	46	36

  

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

1. State the null and alternate hypotheses for treatments.

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

  

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

Also, state the decision rule for blocks.

1. d & e. 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.)

6. Give your decision regarding the two sets of hypotheses.

Answer 1

a)

null hypothesis": Ho: 1 =2

alternate hypothesis": Ha: 1 2

b)

decision rule for treatments :reject Ho if F> 18.5

c)

for blocks: Ho :1 =2=3

alternate hypothesis: at least one block means differ,

decision rule for blocks :reject Ho if F> 19.0

Source of Variation	SS	df	MS	F
Blocks	192.333	2	96.167	192.33
treatments	181.500	1	181.500	363.00
Error	1.000	2	0.500
Total	374.833	5

f)

for treatments: reject Ho treatment means differ

for blocks: reject Ho: , block means differ