A physics instructor investigates the relationship between the time, t t\,t hours, spent by 8 students on an independent research project and their final ranking, rrr, in a national competition. The data are recorded in the table below, with rank 1 representing the highest level of achievement.
| Student | Research Time (ttt) | Time Rank (xxx) | Competition Rank (rrr) |
|---|---|---|---|
| A | 12 | 7 | 6 |
| B | 45 | 2 | 3 |
| C | 30 | 5 | |
| D | 18 | 7 | |
| E | 55 | 1 | 1 |
| F | 8 | 8 | |
| G | 22 | 4 | |
| H | 38 | 3 | 2 |
Complete the ranks for the research time (assigning rank 1 to the longest time) and calculate the Spearman's rank correlation coefficient for this data.
Stating your hypotheses clearly, test at the 5% level of significance whether there is a positive correlation between the time spent on research and the competition performance. (The critical value for n=8n=8n=8 at the 5% significance level is 0.6429).
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.