| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Single sample confidence interval t-distribution |
| Difficulty | Standard +0.3 This is a straightforward one-sample t-test with clearly stated hypotheses and standard confidence interval calculation. Students must calculate sample mean and variance from summary statistics, then apply routine t-test procedures. While it requires multiple steps and careful calculation, it follows a standard template with no conceptual surprises, making it slightly easier than average for Further Maths statistics. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
9 A farmer grows large amounts of a certain crop. On average, the yield per plant has been 0.75 kg . The farmer has improved the soil in which the crop grows, and she claims that the yield per plant has increased. A random sample of 10 plants grown in the improved soil is chosen. The yields, $x \mathrm {~kg}$, are summarised as follows.
$$\Sigma x = 7.85 \quad \Sigma x ^ { 2 } = 6.19$$
(i) Test at the $5 \%$ significance level whether the farmer's claim is justified, assuming a normal distribution.\\
(ii) Find a 95\% confidence interval for the population mean yield for plants grown in the new soil.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q9 [10]}}