The following table displays the amount of nitrogen supplement added to the soil, xxx (kg/hectare), and the resulting yield of a specific variety of beetroot, www (tonnes/hectare), for a random sample of 6 test plots.
| Plot | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Nitrogen (xxx) | 10 | 50 | 30 | 70 | 20 | 40 |
| Yield (www) | 1.2 | 2.8 | 2.0 | 3.2 | 1.5 | 1.9 |
(You may use Sxx=2333.33S_{xx} = 2333.33Sxx=2333.33, Sww=2.92S_{ww} = 2.92Sww=2.92, Sxw=80S_{xw} = 80Sxw=80)
Test, at the 5% level of significance, whether there is evidence of a correlation between the amount of nitrogen and the beetroot yield using the product moment correlation coefficient (PMCC). State your hypotheses and the critical value used.
Calculate Spearman’s rank correlation coefficient between the rank of nitrogen added and the rank of yield achieved.
Test, at the 5% level of significance, whether there is evidence of a positive correlation between the nitrogen supplement and the yield using Spearman's rank correlation. State your hypotheses and the critical value used.
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.