| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | T-tests (unknown variance) |
| Type | Paired sample t-test |
| Difficulty | Standard +0.3 This is a straightforward paired t-test question requiring students to state hypotheses, calculate differences, perform the test, and state the normality assumption. While it involves multiple steps (8 marks), it's a standard textbook application of a core S4 technique with no novel problem-solving or conceptual challenges—slightly easier than average for A-level. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
As part of an investigation into the effectiveness of solar heating, a pair of houses was identified where the mean weekly fuel consumption was the same. One of the houses was then fitted with solar heating and the other was not. Following the fitting of the solar heating, a random sample of 9 weeks was taken and the table below shows the weekly fuel consumption for each house.
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly, test, at the 5\% level of significance, whether or not there is evidence that the solar heating reduces the mean weekly fuel consumption. [8]
\item State an assumption about weekly fuel consumption that is required to carry out this test. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q3 [9]}}