The strength of concrete used in commercial construction tends to vary from one batch to another. Consequently, small test cylinders of concrete sampled from a batch are "cured" for periods up to about 28 days in temperature and moist controlled environments before strength measurements are made. The accompanying data resulted from an experiment carried out to compare three different curing methods with respect to compression strength (Mpa) on ten batches. Conduct a full factor analysis at alpha equal .05 level of significance to determine effects on batches and methods as well as interaction effects. The compression strengths, Batches and methods or blocks are summarized below:

Treatment Methods	1	2	3	4	5	6	7	8	9	10
A	30.7	29.1	30	31.9	30.5	26.9	28.2	32.4	26.6	28.6
B	33.7	30.6	32.2	34.6	33	29.3	28.4	32.4	29.5	29.4
C	30.5	32.6	30.5	33.5	32.4	27.8	30.7	33.6	29.2	33.2

Answer the following questions as well as questions on the answer sheet.

a. What are the mean compression strength values for each method (Method A, Method B, Method C)

b. State the null hypothesis for the effect on Batch variable, the p value, the calculated F value and decision (accept or reject Ho)

c. State the null hypothesis for the effect on Method variable, the p value, the calculated F and decision (accept or reject Ho)

d. If the null hypothesis is rejected (for either Method or Batch) describe reasons why the test was rejected