| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2002 |
| Session | June |
| 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: calculate differences, state hypotheses, find test statistic, compare to critical value, and conclude. While it requires multiple steps (8 marks), it's a routine application of a core S4 technique with no conceptual surprises or novel problem-solving required. Slightly easier than average due to its textbook nature and clear setup. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
| Car | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Distance without additive | 163 | 172 | 195 | 170 | 183 | 185 | 161 | 176 |
| Distance with additive | 168 | 185 | 187 | 172 | 180 | 189 | 172 | 175 |
A chemist has developed a fuel additive and claims that it reduces the fuel consumption of cars. To test this claim, 8 randomly selected cars were each filled with 20 litres of fuel and driven around a race circuit. Each car was tested twice, once with the additive and once without. The distances, in miles, that each car travelled before running out of fuel are given in the table below.
\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
\hline
Car & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
Distance without additive & 163 & 172 & 195 & 170 & 183 & 185 & 161 & 176 \\
\hline
Distance with additive & 168 & 185 & 187 & 172 & 180 & 189 & 172 & 175 \\
\hline
\end{tabular}
Assuming that the distances travelled follow a normal distribution and stating your hypotheses clearly test, at the 10% level of significance, whether or not there is evidence to support the chemist's claim.
[8]
\hfill \mbox{\textit{Edexcel S4 2002 Q2 [8]}}