Imagine an automobile company looking for additives that might increase gas mileage. As a pilot study , they send 30 cars fueled with a new additive on a road trip from Boston to Los Angeles. Without the additive, those cars are lmown to average 25.0mpg with a standard deviation of 2.4 mpg. Suppose it turns out that the thirty cars averaged 26.3 mpg with the additive. a) What should the company conclude? Is the additive effective? Let a=0.01. Use three methods : the p-value , the critical value approach and the condence Interval method. b) Find the power of the test when u is actually (i) 25.750 (ii) 26.8 What effect does increasing the distance between the true value of u and hypothesized value u=25 c) Find the power of the test when u is actually 25.750 and n=100 ,a=0.01. What e'ect does increasing the sample size have on the power of the test? (1) Find the power of the test when p. is actually 25.750 and n=30. What effect does increasing alpha have on the power (f the test? Use (1:0.05 . e) What would be the effect on power when u is actually 25.750 ( n=30, 0L=0.01) if 6 could be reduced from 2.4 mpg to 1.2 mpg