Question

A randomized block design yielded the following ANOVA table. Source df SS MS F Treatments 4 501 125.25 9.109 Blocks 2 1 225 112.50 8.182 Error 8 110 13.75 Total 14 836 A. How many blocks and treatments were used in the experiment? B. How many observations were collected in the experiment? C. Specify the null and alternative hypothesis you may use to compare the treatment means. D. Conduct the test of hypothesis and comment on the result. Use a = 0.10.

Answer 1

A.

Number of blocks = df blocks + 1 = 2 + 1 = 3

Number of treatments = df treatments + 1 = 4 + 1 = 5

B.

Number of observations = df Total + 1 = 14 + 1 = 15

C.

The appropriate hypotheses for treatments are,

Null Hypothesis H0T: The means for each treatments are equal.

Alternative Hypothesis H1T: Not all means for each treatments are equal.

The appropriate hypotheses for blocks are,

Null Hypothesis H0T: The means for each blocks are equal.

Alternative Hypothesis H1T: Not all means for each blocks are equal.

D.

Numerator df for treatments = 4

Denominator df = 8

Critical value of F at $\alpha$ = 0.10 and df = 4, 8 is 2.81

Since the observed F (9.109) is greater than the critical value, we reject the null hypothesis H0 and conclude that there is strong evidence that not all means for each treatments are equal.

Numerator df for blocks = 2

Denominator df = 8

Critical value of F at $\alpha$ = 0.10 and df = 2, 8 is 3.11

Since the observed F (8.182) is greater than the critical value, we reject the null hypothesis H0 and conclude that there is strong evidence that not all means for each blocks are equal.