6.75 Are the measurements similar? Refer to Exercise 6.30 (page 360). 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.
| 5.0 | 6.5 | −0.6 | 1.7 | 3.7 | 4.5 | 8.0 | 2.2 | 4.9 | 3.0 |
| 4.4 | 0.1 | 3.0 | 1.1 | 1.1 | 5.0 | 2.1 | 3.7 | −0.6 | −4.2 |
(a) State the appropriate H0 and Ha to test this suspicion.
(b) Carry out the test. Give the P-value, and then interpret the result in plain language.