A randomized block design yielded the ANOVA table to the right. Complete parts a

Question

A randomized block design yielded the ANOVA table to the right. Complete parts a through g.

Source             df                     SS                    MS                  F

Treatments      3                      800                  266.67             28.582

Blocks             4                      204                  51.0                 5.466

Error                12                    112                  9.33

Total                19                    1116

a. How many blocks and treatments were used in the experiment?

There were       blocks and       treatments used.

b. How many observations were collected in the experiment?

n=

c. Specify the null and alternative hypotheses you would use to compare the treatment means. Choose the correct answer below.

A.Upper H0: 1=2=3=4=5

vs. Upper H Subscript aHa: At least two treatment means differ.

B.Upper H 0: 1=2=3

vs. Upper H Subscript aHa: All of the treatment means differ.

C.Upper H0: 1=2=3=4

vs. Upper H Subscript aHa: None of the treatment means differ.

D.Upper H0:1=2=3=4=5=6

vs. Upper H Subscript aHa: At least two treatment means differ.

d. What test statistic should be used to conduct the hypothesis test?

A. F=1.821

B. F=5.466

C. F=7.143

D. F=28.582

e. Specify the rejection region for the tests of parts c and

d. Use =0.01.

Choose the correct answer below.

A. The rejection region is F<5.95.

B. The rejection region is F<5.09

C. The rejection region is F<4.56

D. The rejection region is F>5.09

E. The rejection region is F<5.41

F. The rejection region is F>5.95

G. The rejection region is F>5.41

H. The rejection region is F>4.56.

f. Conduct the test of parts c-e, and state the proper conclusion.

A. Reject Upper H 0. There is insufficient evidence to indicate that at least two treatment means differ.

B. Do not reject Upper H 0.There is insufficient evidence to indicate that at least two treatment means differ.

C. Do not reject Upper H 0. There is sufficient evidence to indicate that at least two treatment means differ.

D. Reject Upper H 0. There is sufficient evidence to indicate that at least two treatment means differ.

g. What assumptions are necessary to ensure the validity of the test you conducted in part f?

A. The distributions of observations corresponding to all the block-treatment combinations are not normal, and their variances are equal.

B. The distributions of observations corresponding to all the block-treatment combinations are not normal, and their variances are not equal.

C. The distributions of observations corresponding to all the block-treatment combinations are normal, and their variances are not equal.

D. The distributions of observations corresponding to all the block-treatment combinations are normal, and their variances are equal.

Explanation / Answer

a) Number of treatment =4

Number of blocks= 5

b)Number of observations were collected in the experiment is 20

c)H0: 1=2=3=4 vs. Ha: None of the treatment means differ.

d) test statistic should be used to conduct the hypothesis test is 28.582

e)Critical value of F for (3,12) d.f at 0.01 level of significance is 5.95.The rejection region is F>5.95.

f) Reject H0. There is sufficient evidence to indicate that at least two treatment means differ.

g)ssumptions are necessary to ensure the validity of the test is

The distributions of observations corresponding to all the block-treatment combinations are normal, and their variances are equal.

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