| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Year | 2019 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared goodness of fit: Uniform |
| Difficulty | Standard +0.3 This is a straightforward chi-squared goodness of fit test with clear structure. Part (a) requires interpreting given output (stating H₀ and comparing p-value to significance level). Part (b) is a standard textbook application: calculate expected frequencies (75/12), compute test statistic, compare to critical value. No conceptual challenges or novel insights required—purely routine application of the chi-squared test procedure. |
| Spec | 5.06b Fit prescribed distribution: chi-squared test5.06c Fit other distributions: discrete and continuous |
| A | B | c | D | |
| 1 | Birth Month | Observed | Expected | Chi-Squared Contributions |
| 2 | Jan-Mar | 259 | 217.25 | 8.023302647 |
| 3 | Apr-June | 232 | 217.25 | 1.001438435 |
| 4 | Jul-Sept | 200 | 217.25 | 1.369677791 |
| 5 | Oct-Dec | 178 | 217.25 | 7.091196778 |
| 6 | Total | 869 | 869 | 17.48561565 |
| 7 | ||||
| 8 | p value | |||
| 9 | 0.000561458 | |||
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
| 3 | 7 | 11 | 4 | 12 | 2 | 6 | 6 | 5 | 8 | 5 | 6 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | Oct-Dec | 178 |
Question 5:
5 | Oct-Dec | 178 | 217.255. Chris is investigating the distribution of birth months for ice hockey players. He collects data for 869 randomly chosen National Hockey League (NHL) players. He decides to carry out a chi-squared test. Using a spreadsheet, he produces the following output.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
& A & B & c & D \\
\hline
1 & Birth Month & Observed & Expected & Chi-Squared Contributions \\
\hline
2 & Jan-Mar & 259 & 217.25 & 8.023302647 \\
\hline
3 & Apr-June & 232 & 217.25 & 1.001438435 \\
\hline
4 & Jul-Sept & 200 & 217.25 & 1.369677791 \\
\hline
5 & Oct-Dec & 178 & 217.25 & 7.091196778 \\
\hline
6 & Total & 869 & 869 & 17.48561565 \\
\hline
7 & & & & \\
\hline
8 & & & p value & \\
\hline
9 & & & 0.000561458 & \\
\hline
& & & & \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item By considering the output, state the null hypothesis that Chris is testing. State what conclusion Chris should reach and explain why.
Chris now wonders if Premier League football players' birth months are distributed uniformly throughout the year. He collects the birth months of 75 randomly selected Premier League footballers. This information is shown in the table below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Jan & Feb & Mar & Apr & May & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\
\hline
3 & 7 & 11 & 4 & 12 & 2 & 6 & 6 & 5 & 8 & 5 & 6 \\
\hline
\end{tabular}
\end{center}
\item Carry out the chi-squared goodness of fit test at the 10\% significance level that Chris should use to conduct his investigation.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 2019 Q5 [11]}}