The question
Name: ______________________ Date: ____________ A fuel additive for city buses (10 points)
Graph
Fuel economy with and without an additive
A city's transit agency runs a fleet of 400 buses. To test a fuel additive, it selected 12 buses at random. Each bus ran one week on regular fuel and one week on fuel with the additive, in a randomly chosen order, on its usual route. The table gives fuel economy in miles per gallon (invented data), and the dotplot shows the 12 differences (with additive minus without).
The maker of the additive claims it raises mean fuel economy by more than 0.5 miles per gallon.
| Bus | Without | With | Difference (with minus without) |
|---|---|---|---|
| 1 | 6.1 | 7 | 0.9 |
| 2 | 5.8 | 6.1 | 0.3 |
| 3 | 6.4 | 7.4 | 1 |
| 4 | 5.5 | 6.1 | 0.6 |
| 5 | 6.9 | 7.4 | 0.5 |
| 6 | 6.2 | 7 | 0.8 |
| 7 | 5.9 | 5.8 | -0.1 |
| 8 | 6.6 | 7.3 | 0.7 |
| 9 | 5.7 | 6.9 | 1.2 |
| 10 | 6.3 | 6.7 | 0.4 |
| 11 | 6 | 6.9 | 0.9 |
| 12 | 6.5 | 7.1 | 0.6 |
(a) Identify the appropriate inference procedure for estimating how much the additive changes mean fuel economy, and define the parameter it estimates in context. [2 points]
(b) Justify that the conditions for the procedure in part (a) are met. [3 points]
(c) Construct a 95% confidence interval for the parameter you defined in part (a). Show your work. [3 points]
(d) Interpret your interval in context. Then explain whether the interval supports the maker's claim that the additive raises mean fuel economy by more than 0.5 miles per gallon. [2 points]