Standard +0.3 This is a structured chi-squared test question with guided parts requiring standard procedures: stating hypotheses, calculating test statistic from given data, comparing to critical values, and interpreting results. While it involves multiple parts, each step follows routine S2 methodology without requiring novel insight or complex problem-solving, making it slightly easier than average.
Find the value of the test statistic, \(X ^ { 2 }\), giving your answer to one decimal place.
State, in context, the conclusion that Emily should reach based on the results of her \(\chi ^ { 2 }\) test.
Make one comment on the GCSE performances of 16-year-old students attending Bailey Language School.
Emily's friend, Joanna, used the same data to correctly conduct a \(\chi ^ { 2 }\) test using the \(10 \%\) level of significance.
State, with justification, the conclusion that Joanna should reach.
\begin{enumerate}[label=(\alph*)]
\item State the null hypothesis that Emily used.
\item Find the value of the test statistic, $X ^ { 2 }$, giving your answer to one decimal place.
\item State, in context, the conclusion that Emily should reach based on the results of her $\chi ^ { 2 }$ test.
\item Make one comment on the GCSE performances of 16-year-old students attending Bailey Language School.
\item Emily's friend, Joanna, used the same data to correctly conduct a $\chi ^ { 2 }$ test using the $10 \%$ level of significance.
State, with justification, the conclusion that Joanna should reach.
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2011 Q3 [10]}}