Worked solution
Estimate emissions mean and variance from test data
A manufacturer launches the environmentally marketed “Green Leaf” car and claims its carbon emission is at most 80 g/km. The transport authority suspects this figure is understated and requests test data from 20 units:
| Carbon emission (g/km) | 78 | 79 | 80 | 81 | 82 |
|---|---|---|---|---|---|
| Number of units | 2 | 3 | 6 | 4 | 5 |
Calculate unbiased estimates of the population mean and variance. marks
[2016/PJC/II/10(i)]
CJC · Review problems · Question 1
Answer
Mean g/km; unbiased variance (g/km)².
Use the frequency-weighted summaries
The sample has , and . Thus g/km and (g/km)². The printed calculator method squares its sample standard deviation to obtain the variance.
How did this part go?
Common mistakes
The task asks for estimates, not a hypothesis test of the manufacturer’s claim.