Question: Professor Shiningstar, a respected professor of electrical engineering was commissioned by the Concerned Consumers Association to test the lifetime of four equally priced fluorescent light bulbs manufactured by four competing companies. Initially, Professor Shiningstar tested a random sample of twelve bulbs from each manufacturer. However due to some unforeseen circumstances some of the results were deemed unreliable, and, as a consequence, had to be discarded. The remaining results were as follows: (Note: The results were coded for convenience)

(a) Find (i) the Total Sum of Squares (ii) the Treatment Sum of Squares and (iii) the Error Sum of Squares.

(b) Test the hypothesis that the mean lifetime of the four makes of light bulbs is the same against the alternative that they are different. Let α=0.05. State , clearly and neatly, any assumptions you need to make.