| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2020 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | Critical region determination |
| Difficulty | Moderate -0.3 This is a straightforward hypothesis testing question requiring standard procedures: stating H₀ and H₁ for a one-tailed test, then finding a critical value from normal tables with known σ. It's slightly below average difficulty as it involves routine application of A-level statistics methods with no problem-solving insight required, though the multi-step calculation and correct interpretation of a one-tailed test at 2.5% prevents it from being trivially easy. |
| Spec | 2.05e Hypothesis test for normal mean: known variance |
In the past, the time for Jeff's journey to work had mean 45.7 minutes and standard deviation 5.6 minutes. This year he is trying a new route. In order to test whether the new route has reduced his journey time, Jeff finds the mean time for a random sample of 30 journeys using the new route. He carries out a hypothesis test at the 2.5% significance level.
Jeff assumes that, for the new route, the journey time has a normal distribution with standard deviation 5.6 minutes.
\begin{enumerate}[label=(\alph*)]
\item State appropriate null and alternative hypotheses for the test. [2]
\item Determine the rejection region for the test. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2020 Q12 [6]}}