An environmental scientist monitors the turbidity of water, TTT (NTU), and the human population density, PPP (people per km2^22), in the surrounding river basins across six different geographical zones. The results for the six zones are shown in the table below.
| Zone | Alpha | Beta | Gamma | Delta | Epsilon | Zeta |
|---|---|---|---|---|---|---|
| Turbidity, TTT | 2.4 | 5.2 | 8.1 | 12.0 | 15.6 | 19.8 |
| Population Density, PPP | 110 | 450 | 240 | 680 | 1150 | 920 |
(You may use STT=214.21S_{TT} = 214.21STT=214.21, SPP=803083.33S_{PP} = 803083.33SPP=803083.33, STP=11529.83S_{TP} = 11529.83STP=11529.83)
Test, at the 5% level of significance, whether there is evidence of a non-zero correlation between water turbidity and population density 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 water turbidity and the rank of population density.
Test, at the 5% level of significance, whether there is evidence of a positive correlation between water turbidity and population density 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.