Four factors are thought to possibly influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be run at two levels, producing a 24 design. At each run in the design, samples of the beverage are given to a test panel consisting of 20 people. Each tester assigns a point score from 1 to 10 to the beverage. Total score is the response variable, and the objective is to find a formulation that maximizes total score. Two replicates of this design are run, and the results are shown below.
|
Test
|
Replicate
|
Sample Variance,S2i
|
|
I
|
II
|
|
|
1
|
188
|
195
|
|
|
2
|
172
|
180
|
|
|
3
|
179
|
187
|
|
|
4
|
185
|
178
|
|
|
5
|
175
|
180
|
|
|
6
|
183
|
178
|
|
|
7
|
190
|
180
|
|
|
8
|
175
|
168
|
|
|
9
|
200
|
193
|
|
|
10
|
170
|
178
|
|
|
11
|
189
|
181
|
|
|
12
|
183
|
188
|
|
|
13
|
201
|
188
|
|
|
14
|
181
|
173
|
|
|
15
|
189
|
182
|
|
|
16
|
178
|
182
|
|
QUESTION 1 - - continued:
a. Calculate the effect estimates.
b. Based on the replication of each test condition, calculate S2p and use it to determine the sample variance of an effect.
c. Develop 95% confidence intervals for each effect estimate. Find the statistically significant effects.
d. Write down the appropriate mathematical model, including only those terms found to be statistically significant.
e. Use Bartlett's test to check the homogeneity of the variance of the response.
f. Construct an ANOVA table to see if the variation between the tests is statistically significant.
g. Construct an ANOVA table to identify which of the effect estimates are statistically significant
h. Develop a model for the response based on the results of part (g)
i. Construct an ANOVA table to see if the model developed suffers from lack of fit