A climatologist is investigating the relationship between the altitude, hhh km, at which a sensor is placed and the intensity of cosmic rays, ccc counts per minute (cpm), detected. The climatologist collects data from 8 distinct high-altitude balloons. The results are recorded in the table below.
| Altitude hhh (km) | 1.1 | 2.4 | 3.5 | 4.2 | 5.8 | 6.5 | 8.1 | 10.3 |
|---|---|---|---|---|---|---|---|---|
| Intensity ccc (cpm) | 210 | 340 | 420 | 510 | 800 | 760 | 1200 | 1550 |
Calculate Spearman's rank correlation coefficient for these data.
The climatologist believes that there is a positive correlation between altitude and cosmic ray intensity. Stating your hypotheses clearly, test this belief at the 5% level of significance.
State the required condition for a product moment correlation coefficient (PMCC) to be a valid test of association between these two variables.
For this sample, the mean intensity is 723.75 cpm and the median intensity is 635 cpm. Explain whether these statistics suggest that the condition stated in part (c) is likely to be met.