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.
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.