Here is an ANOVA table from a randomized experiment studying four treatments with n = 3 replicates each.

Df Sum Sq Mean Sq F value Pr(>F)

Treatment 3 80.25 26.75.2.8919 0.1021

Residuals 874.00.9.25

Total.11 154.25

(a) Write down the (fixed) effects model:

(b) The estimate of error variance 2 is

(c) Let i be the estimate of i , the mean response of treatment i. The variance of i is

(d) The estimated standard error of i is

(e) What are the null and alternative hypotheses of interest?

(f) Are the treatments significantly different at 5% level? Why?

(g) Suppose that this experiment had been conducted in a randomized block design, and that the sum of squares for blocks was 30. Complete the ANOVA table to show the correct analysis for a randomized block design below:

Source DF Sum Sq Mean Sq F

Treatment

Block 30

Residuals

Total