Standard +0.3 This is a standard chi-squared test of independence with a 2×3 contingency table, requiring routine calculation of expected frequencies, test statistic, and comparison with critical value. Part (b) tests understanding of the condition that expected frequencies should be ≥5. While it requires multiple computational steps, it follows a completely standard procedure taught in S3 with no novel insight needed, making it slightly easier than average.
The Director of Studies at a large college believed that students' grades in Mathematics were independent of their grades in English. She examined the results of a random group of candidates who had studied both subjects and she recorded the number of candidates in each of the 6 categories shown.
Maths grade A or B
Maths grade C or D
Maths grade E or U
English grade A or B
25
25
10
English grade C to U
15
30
15
Stating your hypotheses clearly, test the Director's belief using a \(10 \%\) level of significance. You must show each step of your working.
The Head of English suggested that the Director was losing accuracy by combining the English grades C to U in one row. He suggested that the Director should split the English grades into two rows, grades C or D and grades E or U as for Mathematics.
State why this might lead to problems in performing the test.
\begin{enumerate}
\item The Director of Studies at a large college believed that students' grades in Mathematics were independent of their grades in English. She examined the results of a random group of candidates who had studied both subjects and she recorded the number of candidates in each of the 6 categories shown.
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& Maths grade A or B & Maths grade C or D & Maths grade E or U \\
\hline
English grade A or B & 25 & 25 & 10 \\
\hline
English grade C to U & 15 & 30 & 15 \\
\hline
\end{tabular}
\end{center}
(a) Stating your hypotheses clearly, test the Director's belief using a $10 \%$ level of significance. You must show each step of your working.
The Head of English suggested that the Director was losing accuracy by combining the English grades C to U in one row. He suggested that the Director should split the English grades into two rows, grades C or D and grades E or U as for Mathematics.\\
(b) State why this might lead to problems in performing the test.
\hfill \mbox{\textit{Edexcel S3 2007 Q2 [10]}}