| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared goodness of fit: Given ratios |
| Difficulty | Standard +0.3 This is a straightforward chi-squared goodness of fit test with given ratios (proportional to number of employees). The expected frequencies are easily calculated by distributing the total incidents proportionally. Part (b) is basic sampling methodology requiring simple explanation. While it requires understanding of the chi-squared test setup, it's a standard textbook application with no novel insight needed, making it slightly easier than average. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc5.06a Chi-squared: contingency tables |
| Warehouse | A | \(B\) | C | D | E |
| Number of employees, (in thousands) | 2 | 1 | 3.8 | 3 | 2.2 |
| Number of reported first aid incidents | 15 | 10 | 40 | 26 | 23 |
4. A company selects a random sample of five of its warehouses. The table below summarises the number of employees, in thousands, at each warehouse and the number of reported first aid incidents at each warehouse during 2017
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Warehouse & A & $B$ & C & D & E \\
\hline
Number of employees, (in thousands) & 2 & 1 & 3.8 & 3 & 2.2 \\
\hline
Number of reported first aid incidents & 15 & 10 & 40 & 26 & 23 \\
\hline
\end{tabular}
\end{center}
The personnel manager claims that the mean number of reported first aid incidents per 1000 employees is the same at each of the company's warehouses.
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly, use a $5 \%$ level of significance to test the manager's claim.
Jean, the safety officer at warehouse $C$, kept a record of each reported first aid incident at warehouse $C$ in 2017. Jean wishes to select a systematic sample of 10 records from warehouse $C$.
\item Explain, in detail, how Jean should obtain such a sample.
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2018 Q4 [9]}}