6. Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second, when pressure drops sufficiently to allow the water to dissociate into water vapor forming a gas bubble behind the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to occur. Nine tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed X = 103.2 meters per second. Assume that speed is normally distributed with known standard deviation of = 4 meters per second.

(a) Test the hypothesis H0: = 100 versus H1: > 100 using = 0.05.

(b) What sample size would be required to detect a true mean speed of 102 meters per second if we wanted the power of the test to be at least 0.90? (Use Minitab)