| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2015 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared goodness of fit |
| Type | Chi-squared test of independence |
| Difficulty | Standard +0.3 This is a standard chi-squared test of independence with clearly structured data requiring conversion of percentages to frequencies, calculation of expected values, and application of the test statistic formula. While it has multiple steps (12 marks), each step follows a routine procedure taught in S3 with no novel insight required, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Male | Female | |
| Distinction | 18.5\% | 27.5\% |
| Merit | 63.5\% | 60.0\% |
| Unsatisfactory | 18.0\% | 12.5\% |
A Head of Department at a large university believes that gender is independent of the grade obtained by students on a Business Foundation course. A random sample was taken of 200 male students and 160 female students who had studied the course.
The results are summarised below.
\begin{tabular}{|c|c|c|}
\hline
& Male & Female \\
\hline
Distinction & 18.5\% & 27.5\% \\
\hline
Merit & 63.5\% & 60.0\% \\
\hline
Unsatisfactory & 18.0\% & 12.5\% \\
\hline
\end{tabular}
Stating your hypotheses clearly, test the Head of Department's belief using a 5\% level of significance. Show your working clearly. [12]
\hfill \mbox{\textit{Edexcel S3 2015 Q5 [12]}}