Question: The makers of the Duracell batteries want to prove that their size AA battery lasts an average of 30 minutes longer than Duracell’s main competitor, the Energizer. Two independent random samples of 50 batteries of each kind are selected, and the batteries are run continuously until they are no longer operational. The sample data are summarized below:

Duracell (1) Energizer(2)

x (Minutes) 308 254

s (Minutes) 84 67

a) Develop and interpret a 95% confidence interval for the difference of the population means? (10 pts)

b) At a=5%, is there evidence to prove that Duracell’s batteries last, on average, 30 minutes longer than the Energizer batteries of the same size?

(10 pts)