A botanist is investigating the relationship between the moisture content of soil, MMM (measured as a percentage), and the final growth height of a specific seedling species, HHH (measured in cm). The data for 8 test plots are recorded in the table below.
| Plot | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Moisture (MMM %) | 25 | 12 | 38 | 55 | 30 | 42 | 18 | 50 |
| Height (HHH cm) | 18.3 | 10.1 | 25.4 | 32.8 | 15.2 | 28.1 | 14.9 | 20.5 |
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 positive correlation between soil moisture content and seedling growth height.
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.