A manufacturer of tires claims that the mean lifetime of these tires is at least 25000 miles when the production process is working properly. Based upon past experience, the standard deviation of the lifetime of the tires is 3500 miles. The

production manager will stop the production if there is evidence that the mean lifetime of the tires is below 25000 miles.

1. If the production manager wishes to have 80% power of detecting a shift in the lifetime mean of the tires from 25000 to 24000 miles and if he is willing to take a 5% risk of committing a Type I error, what sample size must be selected?

2. If the production manager wishes to have 80% power of detecting a shift in the lifetime mean of the tires from 25000 to 23000 miles and if he is willing to take a 5% risk of committing a Type I error, what sample size must be selected?