| Exam Board | Edexcel |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | 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, requiring routine application of the test procedure. While it's a Further Maths topic (making it slightly harder than core), the question follows a highly structured format with parts guiding students through each step: stating hypotheses, calculating expected frequencies, computing the test statistic, and making conclusions. The calculation is straightforward with small numbers, and no conceptual insight beyond textbook procedures is required. |
| Spec | 5.06a Chi-squared: contingency tables |
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | Language | |||
| \cline { 3 - 5 } \multicolumn{2}{c|}{} | French | Spanish | M andarin | |
| \multirow{2}{*}{Gender} | M ale | 23 | 22 | 20 |
| \cline { 2 - 5 } | Female | 38 | 32 | 15 |
| Answer | Marks | Guidance |
|---|---|---|
| Language | French | Spanish |
| Male | 26.43… | 23.4 |
| Female | 34.56… | [30.6] |
# Question 1
## 1(a)
B1: For correct hypothesis in context
$H_0$: There is no association between language and gender
(1 mark)
---
## 1(b)
B1*cso: For a correct calculation leading to the given answer and no errors seen
$\frac{5485}{30.6} \times 150$
(1 mark)
---
## 1(c)
M1: For attempt to find expected frequencies using $\frac{\text{(Row Total)(Column Total)}}{\text{(Grand Total)}}$
Expected frequencies:
| Language | French | Spanish | Mandarin |
|---|---|---|---|
| Male | 26.43… | 23.4 | 15.16… |
| Female | 34.56… | [30.6] | 19.83… |
M1: For applying $\frac{(O-E)^2}{E}$
$\chi^2 = \frac{(23-26.43)^2}{26.43} + \frac{(15-19.83)^2}{19.83} + \ldots$
A1: Awrt 3.6 or 3.7
(3 marks)
---
## 1(d)
M1: For using degrees of freedom to find critical value
Degrees of freedom: $(3-1)(2-1) = 2$
$\chi^2_{2,0.01} = 9.210$
A1: For correct comparison and conclusion
As $\chi^2 < 9.210$, the null hypothesis is not rejected
(2 marks)
---
## 1(e)
B1: For correct conclusion with supporting reason
Still not rejected since $\chi^2 < \chi^2_{2,0.1} = 4.605$
(1 mark)
---
**Total: 8 marks**\begin{enumerate}
\item A university foreign language department carried out a survey of prospective students to find out which of three languages they were most interested in studying.
\end{enumerate}
A random sample of 150 prospective students gave the following results.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & \multicolumn{3}{|c|}{Language} \\
\cline { 3 - 5 }
\multicolumn{2}{c|}{} & French & Spanish & M andarin \\
\hline
\multirow{2}{*}{Gender} & M ale & 23 & 22 & 20 \\
\cline { 2 - 5 }
& Female & 38 & 32 & 15 \\
\hline
\end{tabular}
\end{center}
A test is carried out at the $1 \%$ level of significance to determine whether or not there is an association between gender and choice of language.\\
(a) State the null hypothesis for this test.\\
(b) Show that the expected frequency for females choosing Spanish is 30.6\\
(c) Calculate the test statistic for this test, stating the expected frequencies you have used.\\
(d) State whether or not the null hypothesis is rejected. Justify your answer.\\
(e) Explain whether or not the null hypothesis would be rejected if the test was carried out at the $10 \%$ level of significance.
\section*{Q uestion 1 continued}
\section*{Q uestion 1 continued}
\section*{Q uestion 1 continued}
\hfill \mbox{\textit{Edexcel FS1 AS Q1 [8]}}