| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Comment on claim using CI |
| Difficulty | Moderate -0.3 This is a straightforward application of standard confidence interval formulas with known population standard deviation. Part (a) requires a prediction interval calculation (μ ± 1.96σ), part (b) is a textbook confidence interval for the mean (x̄ ± z*σ/√n), and part (c) asks for basic interpretation by checking if the claimed value falls within the interval. All techniques are routine S3 material with no problem-solving insight required, making it slightly easier than average but not trivial due to the multi-part structure and need to distinguish between population and sampling distributions. |
| Spec | 5.05d Confidence intervals: using normal distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 14 | 19.290 |
Question 2:
2 | 14 | 19.290The heights of a random sample of 10 imported orchids are measured. The mean height of the sample is found to be 20.1 cm. The heights of the orchids are normally distributed.
Given that the population standard deviation is 0.5 cm,
\begin{enumerate}[label=(\alph*)]
\item estimate limits between which 95\% of the heights of the orchids lie, [3]
\item find a 98\% confidence interval for the mean height of the orchids. [4]
\end{enumerate}
A grower claims that the mean height of this type of orchid is 19.5 cm.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Comment on the grower's claim. Give a reason for your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2009 Q2 [9]}}