Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mile
age, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer's calculations of miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer's and the driver's calculations for that random sample of 20 records. The driver wants to determine if these calculations are different. Assume that the standard deviation of a difference is σ = 3.0. 4.0 6.5 −0.6 1.5 3.7 4.5 8.0 2.2 4.7 3.0 4.4 0.1 3.0 1.3 1.3 5.0 2.1 3.8 −0.6 −4.2 (a) State the appropriate H0 and Ha to test this suspicion. H0: μ < 0 mpg; Ha: μ > 0 mpg H0: μ = 3 mpg; Ha: μ ≠ 3 mpg H0: μ > 3 mpg; Ha: μ < 3 mpg H0: μ > 0 mpg; Ha: μ < 0 mpg H0: μ = 0 mpg; Ha: μ ≠ 0 mpg (b) Carry out the test. Give the P-value. (Round your answer to four decimal places.)
