6 A student is investigating the relationship between age and grip strength in adults. The student selects 10 people and records their ages in years and the grip strengths of their dominant hand, measured in kg. The data are shown in the table below, together with a scatter diagram to illustrate the data.
| Age | 22 | 29 | 36 | 39 | 53 | 57 | 60 | 71 | 76 | 82 |
| Grip strength | 38 | 46 | 42 | 49 | 37 | 47 | 36 | 33 | 34 | 24 |
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The student decides to carry out a hypothesis test to investigate whether there is negative association between age and grip strength.
- Explain why the student decides to carry out a test based on Spearman's rank correlation coefficient.
- State what property of the sample is required in order for it to be valid to carry out a hypothesis test.
- In this question you must show detailed reasoning.
Assuming that the property in part (b) holds, carry out the test at the \(5 \%\) significance level.