An aerospace engineer measured the energy density, ddd Wh/kg, of 8 different lithium-sulfur batteries used in high-altitude drones. He coded the data using the transformation w=d−kmw = \frac{d - k}{m}w=md−k, where kkk and mmm are positive constants. His results are shown in the table below.
| ddd | 210 | 195 | 186 | 201 | 192 | 213 | 183 | 204 |
|---|---|---|---|---|---|---|---|---|
| www | 20.0 | 10.0 | 4.0 | 14.0 | 8.0 | 22.0 | 2.0 | 16.0 |
Determine the value of kkk and the value of mmm.
The engineer also recorded the total service time, ttt thousand hours, of each battery. The results are summarised below.
Stt=8.40Sww=340.0Stw=−48.5 S_{tt} = 8.40 \quad S_{ww} = 340.0 \quad S_{tw} = -48.5 Stt=8.40Sww=340.0Stw=−48.5Calculate the product moment correlation coefficient (PMCC) between ttt and www.
Write down the value of the PMCC between ttt and ddd.
The engineer records the total energy capacity and battery mass for 2 additional drones, AAA and BBB.
| Drone | Total Energy Capacity (Wh) | Battery Mass (kg) |
|---|---|---|
| AAA | 48000 | 250 |
| BBB | 39000 | 200 |
Suggest which drone is most likely to have the higher service time. Justify your answer.
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