2. Two plants are to produce certain fluorescent bulbs using new equipment. Because of the similarity to the other processes making fluorescent bulbs of different types, it is known that over wide ranges of μ1 and μ2, the distributions of the life of light bulbs from plants I and II are, respectively, N(μ1, (200)2) and N(μ2, (200)2). The quality control division at each of the two plants took data, and the results for the two random samples produced the following summary statistics:

Plant I : ¯X1 = 1410 hours, n1 = 25 Plant II : ¯X2 = 1260 hours, n2 = 20

(a) Find a 99% confidence interval for δ = μ1 − μ2.

(b) Use the result in

(a) to test the hypothesis H0: δ = 0 against H1: δ = 0 at the 1% level of significance.

9.12 Sequential Tests of Hypotheses 429