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 4 1,014 253.5 43.707

Blocks         5 220 44.0 7.586

Error          20 116 5.8

Total          29 1350

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 H 0H0: mu 1 equals mu 2 equals mu 3 equals mu 4 equals mu 51=2=3=4=5 vs. Upper H Subscript aHa: At least two treatment means differ.

B. Upper H 0H0: mu 1 equals mu 2 equals mu 31=2=3 vs. Upper H Subscript aHa: All of the treatment means differ.

C. Upper H 0H0: mu 1 equals mu 2 equals mu 3 equals mu 41=2=3=4 vs. Upper H Subscript aHa: None of the treatment means differ.

D. Upper H 0H0: mu 1 equals mu 2 equals mu 3 equals mu 4 equals mu 5 equals mu 61=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=43.707

B. F=8.741

C. F=7.586

D. F=1.897

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<4.104.10.

B. The rejection region is F<7.56

C. The rejection region is F<4.43.

D. The rejection region is F>4.43

E. The rejection region is F<5.42

F. The rejection region is F>7.56

G. The rejection region is F>5.42

H. The rejection region is F>4.10.

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

A. Reject Upper H 0H0. There is insufficient evidence to indicate that at least two treatment means differ.

B. Do not reject Upper H 0H0. There is insufficient evidence to indicate that at least two treatment means differ.

C. Do not reject Upper H 0H0. There is sufficient evidence to indicate that at least two treatment means differ.

D. Reject Upper H 0H0. 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 blocks = 6 and Number of treatments= 5

b) Number of observations were collected in the experiment is n= 30

c) H0: 1=2=3=4=5 vs Ha: At least two treatment means differ.

d) test statistic should be used to conduct the hypothesis test is F=43.707

e)critical value of F for (4,20) d.f at 0.01 is 4.43 .The rejection region is F>4.43

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

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

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