| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2020 |
| Session | October |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared test of independence |
| Difficulty | Moderate -0.3 This is a standard chi-squared test of independence with straightforward calculations. Students must complete given (O-E)²/E values, calculate degrees of freedom (2×2=4), find the critical value, and perform a routine hypothesis test. While it requires multiple steps, all procedures are textbook-standard with no novel insight needed, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 2 - 5 } \multicolumn{1}{c|}{} | Arts | Humanities | Sciences | Total |
| Distinction | 22 | 32 | 38 | 92 |
| Merit | 15 | 30 | 13 | 58 |
| Pass | 18 | 15 | 17 | 50 |
| Total | 55 | 77 | 68 |
| \cline { 2 - 5 } \multicolumn{1}{c|}{} | Arts | Humanities | Sciences | Total |
| Distinction | 0.43 | 0.33 | 1.44 | 2.20 |
| Merit | 0.06 | 2.63 | 2.29 | 4.98 |
| Pass | ||||
2. A university awards its graduates a degree in one of three categories, Distinction, Merit or Pass.
Table 1 shows information about a random sample of 200 graduates from three departments, Arts, Humanities and Sciences.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Arts & Humanities & Sciences & Total \\
\hline
Distinction & 22 & 32 & 38 & 92 \\
\hline
Merit & 15 & 30 & 13 & 58 \\
\hline
Pass & 18 & 15 & 17 & 50 \\
\hline
& Total & 55 & 77 & 68 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}
Xiu wants to carry out a test of independence between the category of degree and the department.
Table 2 shows some of the values of $\frac { ( O - E ) ^ { 2 } } { E }$ for this test.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & Arts & Humanities & Sciences & Total \\
\hline
Distinction & 0.43 & 0.33 & 1.44 & 2.20 \\
\hline
Merit & 0.06 & 2.63 & 2.29 & 4.98 \\
\hline
Pass & & & & \\
\hline
\multicolumn{5}{|l|}{} \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Complete Table 2
\item Hence, complete Xiu's hypothesis test using a $5 \%$ level of significance. You should state the hypotheses, the degrees of freedom and the critical value used for this test.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2020 Q2 [9]}}