Supercavitationis 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 speedx =102.2 meters per second. Assume that speed is normally distributed with=4 meters per second. Use=0.05

(a)TestH0:=100

versusH1:<100

cannot reject null hypothesis or reject null hypothesis

(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

(c)What sample size would be required if we want to detect a true mean speed as low as 93 meters per second if we wanted the power of the test to be at least 0.85.