| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | May |
| Marks | 11 |
| Topic | Chi-squared test of independence |
| Type | Interpret association after test |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 3×3 contingency table. Students must calculate expected frequencies, compute chi-squared contributions, compare to critical value, and make a brief interpretation. While it requires multiple computational steps, it follows a completely routine procedure taught in all FM statistics courses with no novel insight required. The interpretation in part (ii) is straightforward comparison of observed vs expected values. Slightly easier than average due to its formulaic nature. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | Working days lost | |||
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | \(\mathbf { 0 }\) to 4 | 5 to 9 | 10 or more | |
| \multirow{3}{*}{Age} | Under 35 | 31 | 27 | 4 |
| \cline { 2 - 5 } | 35 to 50 | 28 | 32 | 8 |
| \cline { 2 - 5 } | Over 50 | 16 | 28 | 16 |
15.
A researcher at a large company thinks that there may be some relationship between the numbers of working days lost due to illness per year and the ages of the workers in the company. The researcher selects a random sample of 190 workers. The ages of the workers and numbers of days lost for a period of 1 year are summarised below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & \multicolumn{3}{|c|}{Working days lost} \\
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & $\mathbf { 0 }$ to 4 & 5 to 9 & 10 or more \\
\hline
\multirow{3}{*}{Age} & Under 35 & 31 & 27 & 4 \\
\cline { 2 - 5 }
& 35 to 50 & 28 & 32 & 8 \\
\cline { 2 - 5 }
& Over 50 & 16 & 28 & 16 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Carry out a test at the $1 \%$ significance level to investigate whether the researcher's belief appears to be true. Your working should include a table showing the contributions of each cell to the test statistic.
\item For the 'Over 50 ' age group, comment briefly on how the working days lost compare with what would be expected if there were no association.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q15 [11]}}