A marine biologist is studying the relationship between ocean depth and water temperature. She takes readings at 10 different sites in a specific region of the North Atlantic. The depth DDD (in metres) and the water temperature TTT (in ∘^{\circ}∘C) are recorded for each site.
| Site | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Depth DDD (m) | 100 | 250 | 400 | 550 | 700 | 850 | 1000 | 1150 | 1300 | 1450 |
| Temp TTT (∘^{\circ}∘C) | 18.5 | 16.1 | 12.4 | 13.2 | 10.5 | 9.1 | 7.4 | 4.8 | 5.2 | 3.9 |
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 negative correlation between ocean depth and water temperature. State the critical value used.
A researcher suggests that if the surface water is artificially heated, the ocean depth at that location will automatically decrease. Comment on this suggestion.
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.