A 2 × 2 × 2 × 2 = 2⁴ factorial experiment was conducted to investigate the effect of four factors on the light output, y, of flashbulbs. Two observations were taken for each of the factorial treatments. The factors are: amount of foil contained in a bulb (100 and 120 milligrams); speed of sealing machine (1.2 and 1.3 revolutions per minute); shift (day or night); machine operator (A or B). The data for the two replications of the 24 factorial experiment are shown below. To simplify computations, let

a. Do the data provide sufficient evidence to indicate that any of the factors contribute information for the prediction of y? Give the results of a statistical test to support your answer.

b. Identify the factors that appear to affect the amount of light y in the flashbulbs.

c. Give the complete factorial model for y.

d. How many degrees of freedom will be available for estimating σ²?

Speed 1.25 X2 = Amount 110 X1 10 .05 so that x and x2 will take values -1 and + 1. Also, if night shift if operator B X3 = X4 = 1 if day shift 1 1 if operator A