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).
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.