4) (28 points) A battery manufacturer claims that its AA size batteries have a true average life of 1425 hours of use and a standard deviation of 80 hours. You wonder if this claim is true. Hence, you decide to test if there is evidence at alpha = .07 that the true average life is different than 1425 hours of use. To do so, you randomly select 81 batteries.

1. If the true average life (_A) is 1405 hours of use, what is the probability of making a Type II Error? (9 points)

1. If the true average life (_A) is 1260 hours of use, what is the probability of making a Type II Error? (9 points)

1. If the sample mean of the 81 randomly selected batteries is 1514, construct a 93% Confidence Interval for mu and use the result to determine whether or not you would reject the null in favor of the alternative. (10 points)