An ecologist investigating the health of a deep freshwater lake believes that the concentration of dissolved oxygen, CCC (mg/L), decreases as the depth, zzz (m), increases. To test this, the ecologist measures the oxygen concentration at eight different depths. The data are shown in the table below.
| Depth zzz (m) | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
|---|---|---|---|---|---|---|---|---|
| Oxygen CCC (mg/L) | 9.8 | 10.5 | 8.1 | 8.4 | 7.0 | 7.2 | 5.4 | 5.9 |
Calculate Spearman's rank correlation coefficient between zzz and CCC.
Stating your hypotheses clearly, test at the 5% level of significance whether or not the data provide support for the ecologist's belief that oxygen concentration decreases as depth increases.
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.