An engineering team is testing the flight endurance of 8 different commercial drones. The table below shows the initial battery charge level, xxx percentage, and the final endurance rank (where rank 1 is the drone that stayed in the air the longest) for each drone during a standardised test flight.
| Drone | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Initial Charge (xxx %) | 98.5 | 94.2 | 96.8 | 92.0 | 88.5 | 90.2 | 85.4 | 82.0 |
| Endurance Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Given that the highest initial charge level is ranked number 1:
Calculate the Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between the rank of the initial battery charge and the endurance rank.
An analyst suggests using the actual flight durations, yyy minutes, instead of ranks. For the 8 drones, it is given that:
Sxx=220.36,Syy=150.0,Sxy=170.87 S_{xx} = 220.36, \quad S_{yy} = 150.0, \quad S_{xy} = 170.87 Sxx=220.36,Syy=150.0,Sxy=170.87Calculate the product moment correlation coefficient (PMCC) between the initial battery charge and the flight duration. Give your answer to 3 decimal places.
Use your PMCC value to test at the 5% level of significance whether there is evidence of a positive correlation between the initial battery charge and the flight duration.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.