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.
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.