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.
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.