Question

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

  

	Treatment
Block	1	2
A	43	35
B	31	20
C	40	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) H0t: There is no significance difference among the treatments

H1t: Not all treatment means are equal

Let the los be alpha = 0.05

b)

H0b: There is no significance difference among the blocks

H1b: Not all block means are equal

Let the los be alpha = 0.05

c) From the given data

	Treatment
Block	1	2	Ti	Ti^2/2
A	43	35	78	3042.000
B	31	20	51	1300.500
C	40	36	76	2888.000
Tj	114	91	205	7230.500
Tj^2/3	4332.000	2760.333	7092.333

ANOVA Table:

From the ANOVA table, F-Ratio of Rows = 18.35, F criitcal value value = 19

since F-Ratio < F critical value so we accept H0b,

Thus we conclude that there is no significance difference among the blocks

From the ANOVA table, F-Ratio of columns = 14.30, F criitcal value value = 118.513

since F-Ratio < F critical value so we accept H0t,

Thus we conclude that there is no significance difference among the treatments