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.
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.