Math Problem Solver

1. An agronomist conducted an experiment where seven cowpea varieties were studied.

She decided that a randomised complete block design was appropriate. The variable

of interest was yield in grams per plot. The results are below:

2

Block

Treatment

1 2 3 4 5 6 7 8

1 73 95 138 154 160 187 113 145

2 88 113 153 177 179 208 120 154

3 117 141 172 223 226 248 169 185

4 62 83 112 154 168 174 82 125

i) Explain the importance of a block in this design.

ii) Use ANOVA to determine whether the data provides sufficient evidence to indicate

a difference in mean yield for the different cowpea varieties. Test using α=0.05.

(SHOW YOUR WORKING).

iii) Setup a 95% confidence interval for the difference between variety 1 and 4. Suppose

prior to conducting the experiment you there was a claim that the true difference in

yield per plot between these two varieties is 20. Do the data support this claim?

iv) Use the Least Significant Difference (LSD) to compare the following variety

means: 3 vs 6; 8 vs 5; and 4 vs 5.

v) Present a summary table of cowpea variety means together with relevant statistics.

2. A laundromat owner was interested in the effects of water temperature (factor B) and brand

of detergent (factor A) on the resistance in terms of loss of weight of a given fabric after a

specified number of wash cycles. The data are as follows:

Factor B

(Temperature)

Factor A (Detergent

brand)

a1 a2 a3

b1 2.3

1.9

3.1

2.6

1.8

2.5

1.5

2.2

3.1

2.6

1.8

2.5

b2 4.3

4.5

3.8

2.9

3.5

3.8

5.4

3.3

5.1

5.3

4.6

4.0

b3 2.5

3.5

2.7

3.8

1.8

2.7

2.6

1.4

4.1

5.2

4.8

5.0

i) State the number of replications and treatment combinations in this experiment.

ii) Provide the statistical model for the experimental design used.

iii) Analyse the data using ANOVA and present your results in an analysis of variance

table.

iv) Test all the effects using α=0.05 and make appropriate conclusions. Follow all the

steps of hypothesis testing.

v) Calculate all standard errors for A, B and AB.