An environmental agency monitors air quality at 8 different urban locations using two different portable sensors, Alpha (AAA) and Beta (BBB). The particulate matter readings (μg/m3\mu g/m^3μg/m3) recorded at the same time are shown in the table below:
| Location | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 |
|---|---|---|---|---|---|---|---|---|
| Sensor Alpha (AAA) | 45 | 32 | 58 | 21 | 15 | 60 | 10 | 25 |
| Sensor Beta (BBB) | 40 | 35 | 50 | 28 | 12 | 65 | 18 | 22 |
Calculate Spearman's rank correlation coefficient for these data.
Test, at the 5% level of significance, whether there is a positive correlation between the readings of the two sensors. State your hypotheses clearly.
Sensor Beta was later found to have a calibration error at Location L2; the reading should have been 40 instead of 35.
Without performing any further calculations, explain the procedure for finding Spearman’s rank correlation coefficient given this change.
