Question

A randomized block design yielded the ANOVA table to the right. Complete parts a through g Source Treatments Blocks Error Total df SS MS F 5 656 131.2 18.743 3 312 1040 14 857 15 105 70 23 1,073 a. How many blocks and treatments were used in the experiment? There were 6 blocks and 5 treatments used. b. How many observations were collected in the experiment? c. Specify the null and alternative hypotheses you would use to compare the treatment means. Choose the correct answer below. O A. Ho: -12H3 H5 vs. H, All of the treatment means differ, OB. Ho H 12 H3 H4 H5 H vs. Hy At least two treatment means differ, O C. Ho: 12H3 vs. Hy: None of the treatment means differ, OD. H: 12 = H3 H4 vs. Hy At least two treatment means differ
plz answer from a to g

Answer 1

a) We know that in randomized block design, df_treatment=no_of_teatment - 1 & df_block=no. of Block - 1

So, no. of Block=3+1=4 & no. of treatment = 5+1=6

b) No. of observation= (No. of treatment) * (No. of block) = 6*4 =24

c) Since the Null hypothesis assumes there is no significant difference among various treatment means & Alternative hypothesis is the complement of the Null Hypothesis.So

(B) H0: µ1=µ2=µ3=µ4=µ5=µ6, H1: At least two treatment differ.

d) F statistic for this hypothesis will be defined as is defined as the ratio of the mean sum of square due to treatment to the Mean sum of square due to error i.e. F=131.2/7=18.743 (B)

e) Tabulated value of F at (5,15) degree of freedom at 0.01 level of significance is equal to 4.56. Thus (D) the rejection region is F>4.56

f) Since calculate F=18.743 is much greater than than than tabulated F=4.56. It implies that we can reject and we can accept H1. H0.  (C) Reject H0. There is sufficient evidence to indicate that at least two treatment means differ.

g) Since in any design, The null hypothesis is usually that the variance of the means 0. but from (f) we can see that there is a significant difference among treatment means. It means there is variability among treatment means. So, (D) The distribution of observation corresponding to all the block-treatment combination is normal, and their variances are not equal.