A marine biologist is investigating whether species biodiversity decreases as the depth of a coral reef increases. She maintains a database of 150 identified reef locations in a protected zone and selects a random sample of 8 sites.
Outline how the biologist should select this random sample of 8 sites.
The biologist recorded the maximum depth (hhh meters) of each reef site and ranked the sites according to their Biodiversity Index (BBB), where 1 represents the highest biodiversity and 8 represents the lowest biodiversity. The results are shown in the table below:
| Site | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Depth hhh (m) | 54 | 12 | 33 | 45 | 8 | 22 | 60 | 28 |
| Biodiversity Rank BBB | 8 | 2 | 5 | 7 | 1 | 4 | 6 | 3 |
Calculate Spearman's rank correlation coefficient for these data, ranking depth such that 1 is the deepest reef.
Test the biologist's claim at a 5% level of significance. State your hypotheses clearly. (The critical value for n=8n=8n=8 at the 5% level of significance is 0.6429).
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.