| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×3 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with a 2×3 contingency table. Students need to calculate expected frequencies, compute the test statistic, find critical value from tables, and state conclusion. While it requires multiple steps, it's a routine application of a well-practiced procedure with no conceptual surprises, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Type of holiday | ||||
| \cline { 3 - 5 } \multicolumn{2}{|c|}{} | Self-catering | Hotel | Cruise | |
| \multirow{2}{*}{Salesman} | \(A\) | 25 | 38 | 21 |
| \cline { 2 - 5 } | \(B\) | 28 | 21 | 17 |
8 Two salesmen, $A$ and $B$, work at a company that arranges different types of holidays: self-catering, hotel and cruise. The table shows, for a random sample of 150 holidays, the number of each type arranged by each salesman.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
\multicolumn{2}{|c|}{} & \multicolumn{3}{|c|}{Type of holiday} \\
\cline { 3 - 5 }
\multicolumn{2}{|c|}{} & Self-catering & Hotel & Cruise \\
\hline
\multirow{2}{*}{Salesman} & $A$ & 25 & 38 & 21 \\
\cline { 2 - 5 }
& $B$ & 28 & 21 & 17 \\
\hline
\end{tabular}
\end{center}
Test at the 10\% significance level whether the type of holiday arranged is independent of the salesman.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q8 [8]}}