Consider the data in the table below, which resulted from a designed experiment
ID: 3297747 • Letter: C
Question
Consider the data in the table below, which resulted from a designed experiment in an aluminum smelter. Aluminum is produced by combining alumina with other ingredients in a reaction cell and applying heat by passing electronic current through the cell. Alumina is added continuously to the cell to maintain the proper ratio of alumina to other ingredients. Four different ratio control algorithms were investigated in this experiment. The response variable studied was related to cell voltage. We wish to know if the four different algorithms provide the equal mean voltage. Recognize the DOE method used here is the randomized complete block design (RCBD), where the factor is the radio control algorithm and the block is time period. (a) Write the null hypothesis (H_0) and alternative hypothesis (H_1). (b) Obtain the sums of squares (SS_total, SS_treatments, SS_blocks, SS_error) by clearly showing your work. (c) Develop the ANOVA table (sums of squares, degrees of freedom, mean squares, and F values). (d) Test the hypothesis at the 0.05 level of significance (i.e., alpha = 0.05). In other words, do you reject or FTR (fail to reject) the null hypothesis?Explanation / Answer
a) There are two hypothesis:
One is for blocks and the other is for treatments.Here we are interested in the treatment hypothesis. i.e
H0: mean voltage for algorithm 1 =mean voltage for algo 2= .........=mean voltage for algo 4
V.S
H1: not equal.
b) and c) ANOVA table containing sum of squares and all:
Source DF SS MS F P-value
treatments 3 0.385 0.128333 14.44 0.001
blocks 3 0.825 0.275000 30.94 0.000
Error 9 0.080 0.008889
Total 15 1.290
S = 0.09428 R-Sq = 93.80% R-Sq(adj) = 89.66%
d)When alpha=0.05 we see that treatment p value is 0.001. Hence p value is less than alpha.Hence we reject H0 the null hypothesis.