In an experiment to investigate when a radar picks up a certain kind of target, a total of n = 15 trials arc conducted in which the distance of the target from the radar is measured when the target is detected. A sample mean of x- = 67.42 miles is obtained, with a sample standard deviation of s = 4.947 miles.
(a) Is there enough evidence for the scientists to conclude that the average distance at which the target is detected is at least 65 miles'.'
(b) Construct a 99% one-sided t-interval that provides a lower bound on the average distance at which the target can be detected.