| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Comment on test validity or assumptions |
| Difficulty | Standard +0.3 This is a standard S3 hypothesis testing question following a routine template: calculate mean, find expected frequencies using Poisson probabilities, perform chi-squared goodness-of-fit test. All steps are algorithmic with no novel insight required. While it involves multiple parts and careful calculation, it's easier than average A-level questions because it's purely procedural application of learned techniques with clear signposting. |
| Spec | 5.06c Fit other distributions: discrete and continuous |
| Number of goals | Frequency |
| 0 | 40 |
| 1 | 33 |
| 2 | 14 |
| 3 | 8 |
| 4 | 5 |
| Number of goals | Expected Frequency |
| 0 | 34.994 |
| 1 | \(r\) |
| 2 | \(s\) |
| 3 | 6.752 |
| \(\geqslant 4\) | 2.221 |
The number of goals scored by a football team is recorded for 100 games. The results are summarised in Table 1 below.
\begin{tabular}{|c|c|}
\hline
Number of goals & Frequency \\
\hline
0 & 40 \\
\hline
1 & 33 \\
\hline
2 & 14 \\
\hline
3 & 8 \\
\hline
4 & 5 \\
\hline
\end{tabular}
Table 1
\begin{enumerate}[label=(\alph*)]
\item Calculate the mean number of goals scored per game. [2]
\end{enumerate}
The manager claimed that the number of goals scored per match follows a Poisson distribution. He used the answer in part (a) to calculate the expected frequencies given in Table 2.
\begin{tabular}{|c|c|}
\hline
Number of goals & Expected Frequency \\
\hline
0 & 34.994 \\
\hline
1 & $r$ \\
\hline
2 & $s$ \\
\hline
3 & 6.752 \\
\hline
$\geqslant 4$ & 2.221 \\
\hline
\end{tabular}
Table 2
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $r$ and the value of $s$ giving your answers to 3 decimal places. [3]
\item Stating your hypotheses clearly, use a 5\% level of significance to test the manager's claim. [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2009 Q5 [12]}}