A research laboratory is investigating the relationship between the toxicity of 10 experimental chemical compounds and their production costs. The toxicity of each compound is ranked from 1 (most toxic) to 10 (least toxic). The table below displays the toxicity rank and the production cost per gram (CCC) for each compound, along with some initial cost rankings (assigning rank 1 to the highest cost).
| Compound | Toxicity Rank (TTT) | Production Cost (CCC) | Cost Rank |
|---|---|---|---|
| A | 7 | 42.20 | 8 |
| B | 3 | 105.30 | 2 |
| C | 1 | 112.00 | |
| D | 5 | 67.80 | |
| E | 10 | 25.10 | |
| F | 2 | 98.40 | |
| G | 4 | 85.50 | |
| H | 8 | 55.00 | |
| I | 6 | 74.60 | |
| J | 9 | 33.90 |
By completing the rankings for the production costs, calculate Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the 5% level of significance whether or not there is a positive correlation between toxicity and production cost. (The critical value for n=10n=10n=10 at a 5% significance level is 0.5636).
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.