| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Paired sample t-test |
| Difficulty | Standard +0.3 This is a standard paired t-test question with clear structure: students must recognize the paired design, calculate differences, state hypotheses correctly, find the test statistic, and compare to critical value. While it requires multiple steps and proper hypothesis testing procedure, it's a routine S4 application with no conceptual surprises—slightly easier than average since the paired design is strongly signaled by the context and the calculations are straightforward. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Orange | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Machine A | 60 | 58 | 55 | 53 | 52 | 51 | 54 | 56 |
| Machine B | 61 | 60 | 58 | 52 | 55 | 50 | 52 | 58 |
Manuel is planning to buy a new machine to squeeze oranges in his cafe and he has two models, at the same price, on trial. The manufacturers of machine B claim that their machine produces more juice from an orange than machine A. To test this claim Manuel takes a random sample of 8 oranges, cuts them in half and puts one half in machine A and the other half in machine B. The amount of juice, in ml, produced by each machine is given in the table below.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
Orange & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
Machine A & 60 & 58 & 55 & 53 & 52 & 51 & 54 & 56 \\
\hline
Machine B & 61 & 60 & 58 & 52 & 55 & 50 & 52 & 58 \\
\hline
\end{tabular}
Stating your hypotheses clearly, test, at the 10\% level of significance, whether or not the mean amount of juice produced by machine B is more than the mean amount produced by machine A.
[8]
\hfill \mbox{\textit{Edexcel S4 Q3 [8]}}