2. A teacher believes that those of her students with strong mathematical ability may also have enhanced short-term memory. She shows a random sample of 11 students a tray of different objects for eight seconds and then asks them to write down as many of the objects as they can remember. The results, along with their percentage score in a recent mathematics test, are given in the table below.
| Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) | \(K\) |
| No. of objects | 8 | 11 | 9 | 15 | 17 | 6 | 10 | 14 | 12 | 13 | 5 |
| \% in maths test | 30 | 62 | 57 | 80 | 75 | 43 | 65 | 51 | 48 | 55 | 32 |
- Calculate Spearman's rank correlation coefficient for these data. Show your working clearly.
- Stating your hypotheses clearly, carry out a suitable test to assess the teacher's belief. Use a \(5 \%\) level of significance and state your critical value.
The teacher shows these results to her class and argues that spending more time trying to improve their short-term memory would improve their mathematical ability.
- Explain whether or not you agree with the teacher's argument.