A logistics company is testing a new aerodynamic wing designed to reduce fuel consumption in its fleet of long-haul trucks. To evaluate its effectiveness, 10 trucks are selected. Each truck's fuel consumption (measured in litres per 100km) is recorded over a specific 500km route twice: once using the standard configuration and once with the aerodynamic wing installed. The results are shown in the table below.
| Truck | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Standard | 32.4 | 30.5 | 31.8 | 33.2 | 30.9 | 31.5 | 32.8 | 29.9 | 32.1 | 31.2 |
| Wing | 31.3 | 30.2 | 30.7 | 33.4 | 29.8 | 30.2 | 32.7 | 29.3 | 30.7 | 31.0 |
Stating your hypotheses clearly, test at the 1% level of significance whether there is evidence that the aerodynamic wing reduces the mean fuel consumption. Assume that the differences in fuel consumption follow a normal distribution.
130 exam-style questions on WJEC A Level Maths 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.