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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.