A group of 8 cybersecurity analysts (A, B, C, D, E, F, G, and H) completed a high-stakes penetration testing simulation. Their efficiency scores, where a higher score indicates better performance, are recorded in the table below.
| Analyst | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Efficiency Score | 82 | 45 | 78 | 94 | 36 | 61 | 89 | 52 |
The analysts were also ranked by their years of industry seniority. The list below shows the analysts in order from most senior (rank 1) to least senior (rank 8):
G,D,A,F,C,B,H,E G, \quad D, \quad A, \quad F, \quad C, \quad B, \quad H, \quad E G,D,A,F,C,B,H,ECalculate Spearman's rank correlation coefficient between the analysts' efficiency scores and their seniority ranks.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between seniority and performance efficiency.
The analysts' annual salaries were also recorded. In this dataset, several analysts earned the exact same salary. Explain how you would calculate the Spearman's rank correlation coefficient between efficiency scores and salaries in the presence of these tied values.
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.