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.
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.