In a dairy company they have had problems with the viscosity of a certain chocolate drink. It
Question:
In a dairy company they have had problems with the viscosity of a certain chocolate drink. It is believed that with three ingredients added in small amounts, this problem can be solved, so it is necessary to explore the situation; To do this, a 2 ^ k fractioned experiment with two replicates is run. The following results obtained from this analysis are shown below.
Source | SS | df | MS | F value |
A | 1.62 | 1 | 1.62 | 36 |
B | 2.42 | 1 | 2.42 | 53.77778 |
C | 23.12 | 1 | 23.12 | 513.7778 |
Error | 0.18 | 4 | 0.045 | |
Total | 27.34 | 7 |
Upon seeing this information, the engineer is not very convinced and decides to make a complete 2k design to compare the results obtained in the fractional design, obtaining the following results:
Ingredient A | Ingredient B | Ingredient C | Viscosity | |
-1 | 13.1 | 13.9 | ||
1 | 14.7 | 14.4 | ||
-1 | 14.6 | 14.9 | ||
1 | 14.3 | 14.1 | ||
-1 | 16.9 | 17.2 | ||
1 | 15.5 | 15.1 | ||
-1 | 17.4 | 18.9 | ||
1 | 18.9 | 19.2 |
1.Perform a variance analysis of this data and draw general conclusions
2.Computes residuals, normality, constant variance, and independence
3.Define the model
4.Are the results obtained in the fractional design and in the complete one the same? If so, why?
Mathematical Statistics with Applications in R
ISBN: 978-0124171138
2nd edition
Authors: Chris P. Tsokos, K.M. Ramachandran