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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.