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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.