A high-performance sports scientist is evaluating the efficacy of a new physiological recovery protocol on the lung capacity of elite rowers. The lung capacities, measured in liters, are assumed to be normally distributed. A random sample of 6 rowers underwent the protocol, and their capacities were recorded immediately before and one week after the intervention. The results are presented in the following table:
| Rower | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Before | 6.2 | 5.8 | 7.1 | 6.4 | 5.5 | 6.9 |
| After | 6.5 | 5.7 | 7.4 | 6.2 | 5.8 | 7.2 |
Calculate a 95% confidence interval for the mean difference in lung capacity.
Using your confidence interval, determine whether there is evidence at the 5% significance level to suggest that the protocol has changed the mean lung capacity. State your hypotheses clearly.
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.