A marine biologist is investigating the relationship between water depth and the concentration of a particular micro-organism. Data were collected from 8 different sites, as shown in the table below.
| Site | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Depth (h h\,h m) | 120 | 50 | 250 | 180 | 300 | 100 | 220 | 80 |
| Concentration (C C\,C units/ml) | 3.8 | 2.9 | 6.4 | 7.5 | 9.8 | 4.2 | 6.1 | 2.5 |
Calculate Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between water depth and micro-organism concentration.
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.