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.
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.