| Exam Board | CAIE |
| Module | Further Paper 4 (Further Paper 4) |
| Year | 2023 |
| Session | June |
| Topic | Hypothesis test of a normal distribution |
2 Shane is studying the lengths of the tails of male red kangaroos. He takes a random sample of 14 male red kangaroos and measures the length of the tail, \(x \mathrm {~m}\), for each kangaroo. He then calculates a \(90 \%\) confidence interval for the population mean tail length, \(\mu \mathrm { m }\), of male red kangaroos. He assumes that the tail lengths are normally distributed and finds that \(1.11 \leqslant \mu \leqslant 1.14\).
Find the values of \(\sum x\) and \(\sum x ^ { 2 }\) for this sample.