A sommelier investigates whether the maturation period of single malt whiskey affects its perceived flavor complexity. They select 9 bottles of various ages and rank them based on a 'Complexity Index' (where 9 is the most complex). The results are shown below:
| Age AAA (years) | 45 | 12 | 28 | 15 | 33 | 10 | 21 | 40 | 18 |
|---|---|---|---|---|---|---|---|---|---|
| Complexity Rank CCC | 8 | 2 | 6 | 3 | 9 | 1 | 5 | 7 | 4 |
Calculate Spearman's rank correlation coefficient (rsr_srs) for these data.
Stating your hypotheses clearly and using a one-tailed test at the 5% level of significance, interpret your coefficient. (The critical value for n=9n=9n=9 at the 5% level is 0.6000).
State a reason why Spearman's rank correlation coefficient might be more appropriate than the product moment correlation coefficient (PMCC) for this specific dataset.
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.