An environmental study measured the health of a river system at 7 different locations. At each location, the researchers measured the water temperature, TTT (∘ ^\circ\,∘C), and the dissolved oxygen content, DDD (mg/L). Additionally, a subjective visual pollution rank, VVV, was recorded for each location, where Rank 1 indicates the clearest water and Rank 10 indicates the most debris.
| Location | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| TTT | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
| DDD | 10.2 | 9.4 | 8.1 | 7.3 | 6.4 | 5.5 | 4.2 |
| VVV | 2 | 4 | 5 | 7 | 6 | 9 | 10 |
The following summary statistics are provided: Stt=252S_{tt} = 252Stt=252, Sdd=27.12S_{dd} = 27.12Sdd=27.12, Std=−82.5S_{td} = -82.5Std=−82.5.
Calculate the product moment correlation coefficient (PMCC) between water temperature and dissolved oxygen content.
Use your value from part (a) to test, at the 1% significance level, whether there is evidence of a negative correlation between temperature and dissolved oxygen. State your hypotheses clearly.
State an assumption about the data required for the test in part (b) to be valid.
Calculate the Spearman's rank correlation coefficient between dissolved oxygen content and the visual pollution rank.
Using a 5% level of significance and a two-tailed test, determine whether there is evidence of a correlation between dissolved oxygen and visual pollution rank.
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.