In Practice Problem 12.2 (p. 316), we presented data testing a new gasoline additive. A large number of mileage measurements on the gasoline without the additive showed a mean of 24.7 miles per gallon and a standard deviation of 4.8. An experiment was performed in which 75 cars were tested using the gasoline plus the additive. The results showed a sample mean of 26.5 miles per gallon. To evaluate these data, a directional test with a = 0.051tail was used. Suppose that before doing the experiment, the manufacturer wants to determine the probability that he will be able to detect a real mean increase of 2.0 miles per gallon with the additive if the additive is at least that effective. b. If he increases the N to 75 cars, what is the power to detect a mean increase of 2.0 mile per gallon? Explanation Solution. If N=75 car power to detect a mean increase 2 miles gallon; 4.4 = = 0.554 75 And, XM+= 24.7+ (0.554) (1645) 23.79 then, ZN Now, X-M 23.79-26.5 -= = -4.89 0.554 P(23.71) P(24-9.89) = 0.975