| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Sampling distribution theory |
| Difficulty | Moderate -0.8 This is a conceptual question testing understanding of basic statistical definitions (statistic, sampling distribution) and the key requirement that a statistic cannot depend on unknown population parameters. Parts (a) and (b) require only recall of definitions, while part (c) is straightforward identification that (ii) contains unknown μ and σ. No calculations or problem-solving required, making it easier than average. |
| Spec | 5.05b Unbiased estimates: of population mean and variance |
3. A random sample $X _ { 1 } , X _ { 2 } , \ldots X _ { n }$ is taken from a population with unknown mean $\mu$ and unknown variance $\sigma ^ { 2 }$. A statistic $Y$ is based on this sample.
\begin{enumerate}[label=(\alph*)]
\item Explain what you understand by the statistic $Y$.
\item Explain what you understand by the sampling distribution of $Y$.
\item State, giving a reason which of the following is not a statistic based on this sample.
\begin{enumerate}[label=(\roman*)]
\item $\sum _ { i = 1 } ^ { n } \frac { \left( X _ { i } - \bar { X } \right) ^ { 2 } } { n }$
\item $\sum _ { i = 1 } ^ { n } \left( \frac { X _ { i } - \mu } { \sigma } \right) ^ { 2 }$
\item $\sum _ { i = 1 } ^ { n } X _ { i } ^ { 2 }$
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2009 Q3 [5]}}