In an experiment to investigate the effect of cement factor(number of sacks of cement

Problem 21

In an experiment to investigate the effect of cement factor(number of sacks of cement per cubic yard) on flexural strength of the resulting concrete (Studies of Flexural Strength of Concrete. Part 3: Effects ofVariation in Testing Procedure, Proceedings, ASTM,1957: 11271139), I 5 3 different factor values were used, J 5 5 different batches of cement were selected,and K 5 2 beams were cast from each cement factor/batch combination. Sums of squares include SSA 5 22,941.80, SSB 5 22,765.53, SSE 5 15,253.50,and SST 5 64,954.70. Construct the ANOVA table.Then,assuming a mixed model with cement factor (A) fixed and batches (B) random, test the three pairs of hypotheses of interest at level .05.22. A study was carried out to.

                                                                Step by Step Solution

Step 1 of 3

Given,

I = 3

J = 5

K = 2

The Sums of squares

SSA = 22,941.80

SSB = 22,765.53

SSE = 15,253.50

SST = 64,954.70

Assume the following model:

where the  ’s are independent and normally distributed, each with mean 0 and variance .

 The ’s are referred to as the interaction parameters. The ’s are called the main effects for factor A, and the ’s are the main effects for factor B.

There are three different null hypotheses of interest:

The first, denoted by , states that the different levels of factor A have no effect on true average response. The second, denoted by , asserts that there is no factor B effect. And  is a no-interaction hypothesis.