1 A medical student is investigating the claim that young adults with high diastolic blood pressure tend to have high systolic blood pressure. The student measures the diastolic and systolic blood pressures of a random sample of ten young adults. The data are shown in the table and illustrated in the scatter diagram.
| Diastolic blood pressure | 60 | 61 | 62 | 63 | 73 | 76 | 84 | 87 | 90 | 95 |
| Systolic blood pressure | 98 | 121 | 118 | 114 | 108 | 112 | 132 | 130 | 134 | 139 |
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- Calculate the value of Spearman's rank correlation coefficient for these data.
- Carry out a hypothesis test at the \(5 \%\) significance level to examine whether there is positive association between diastolic blood pressure and systolic blood pressure in the population of young adults.
- Explain why, in the light of the scatter diagram, it might not be valid to carry out a test based on the product moment correlation coefficient.
The product moment correlation coefficient between the diastolic and systolic blood pressures of a random sample of 10 athletes is 0.707 .
- Carry out a hypothesis test at the \(1 \%\) significance level to investigate whether there appears to be positive correlation between these two variables in the population of athletes. You may assume that in this case such a test is valid.