A team of environmental scientists measures the concentration of a specific pollutant (in parts per million, ppm) emitted by eight industrial catalytic converters before and after a specific chemical cleaning process. The emission levels are assumed to be normally distributed. The results for the eight converters are shown in the table below:
| Converter | C1C_1C1 | C2C_2C2 | C3C_3C3 | C4C_4C4 | C5C_5C5 | C6C_6C6 | C7C_7C7 | C8C_8C8 |
|---|---|---|---|---|---|---|---|---|
| Before | 42.5 | 38.8 | 45.2 | 40.1 | 39.5 | 41.4 | 43.6 | 37.9 |
| After | 41.3 | 37.0 | 43.7 | 38.0 | 38.1 | 39.7 | 41.7 | 36.7 |
Calculate a 98% confidence interval for the mean difference in pollutant emissions.
Use your confidence interval to determine whether there is evidence of a change in the mean pollutant emissions. State your hypotheses clearly and provide a reason for your conclusion.
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.