Q1. In a completely randomized design, 10 experimental units were used for the first treatment, 12 for the second treatment, and 19 for the third treatment. Complete the following analysis of variance. Sum of Squares due to Treatments and Sum of Squares Total is computed as 1100 and 1700 respectively. Complete the following analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?
Q2. Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 27 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 9 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,400; SSTR = 4,700.
a) Set up the ANOVA table for this problem.
b) Use α = .01 to test for any significant difference in the means for the three assembly methods.
Q3. To study the effect of temperature on yield in a chemical process, four batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
50 Degrees C 60 Degrees C 70 Degrees C
34 30 23
24 31 28
36 34 28
39 23 30