Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. it occurs above approximately 50 meters per second, when the pressure drops off 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. eight (n = 8) tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed x¯=102.2 meters per second. assume that speed is normally distributed with σ=4 meters per second. use α=0.05. (a) test h0: μ=100 versus h1: μ< 100. choose your answer in accordance to the item a) of the question statement (b) compute the power of this test if the true mean speed is low as 95 meters per second. round your answer to four decimal places (e. g. 98.7654). enter your answer in accordance to the item b) of the question statement (c) what sample size would be required if we want to detect a true mean speed as low as 95 meters per second if we wanted the power of the test to be at least 0.85. enter your answer in accordance to the item c) of the question statement