Consider the data from the first replicate of Exercise 14-15, assuming that four blocks are required. Confound ABD and ABC (and consequently CD) with blocks.

(a) Construct a design with four blocks of four observations each.

(b) Analyze the data.

Exercise 14-15

Four factors are thought to 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 the beverage a point score from 1 to 10. 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 in the table. Analyze the data and draw conclusions. Use a = 0.05 in the statistical tests.

Replicate Treatment Combination II (1) 159 163 168 175 a 158 163 ab 166 168 175 178 179 183 ac bc 173 168 abc 179 182 164 159 ad 187 189 bd 163 159 abd 185 191 cd 168 174 acd 197 199 bcd 170 174 abcd 194 198