A specialty coffee chain evaluates its top 10 baristas based on their internal seniority index (where 1 is the most senior) and their performance in a recent quality control assessment.
| Barista | Seniority Index | Regional Awards | Quality Score |
|---|---|---|---|
| A | 1 | 4 | 82 |
| B | 2 | 2 | 95 |
| C | 3 | 2 | 70 |
| D | 4 | 1 | 88 |
| E | 5 | 2 | 55 |
| F | 6 | 0 | 84 |
| G | 7 | 1 | 62 |
| H | 8 | 0 | 45 |
| I | 9 | 0 | 48 |
| J | 10 | 0 | 75 |
Explain how a researcher should handle the tied values in the 'Regional Awards' column when calculating Spearman's rank correlation coefficient.
Using the 'Quality Score' data (where the highest score is ranked 1), calculate Spearman's rank correlation coefficient, rsr_srs, between the seniority index and the quality score rank.
Test, at the 5% level of significance, whether there is evidence of a positive correlation between seniority and performance quality. State your hypotheses and critical value clearly.
Determine the largest level of significance (from standard statistical tables for n=10n=10n=10) that would lead to a conclusion that there is no evidence of a positive correlation. State the corresponding critical value.
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.