| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | One-tail z-test (lower tail) |
| Difficulty | Moderate -0.3 This is a straightforward one-sample z-test with clearly stated parameters (known variance, sample mean given). Students must state hypotheses, calculate a test statistic using the standard formula, and compare to critical value. It's slightly easier than average because all information is explicitly provided and the procedure is routine, though it requires correct application of the normal distribution and understanding of hypothesis testing mechanics. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
\begin{enumerate}
\item The time, in minutes, it takes Robert to complete the puzzle in his morning newspaper each day is normally distributed with mean 18 and standard deviation 3. After taking a holiday, Robert records the times taken to complete a random sample of 15 puzzles and he finds that the mean time is 16.5 minutes. You may assume that the holiday has not changed the standard deviation of times taken to complete the puzzle.
\end{enumerate}
Stating your hypotheses clearly test, at the $5 \%$ level of significance, whether or not there has been a reduction in the mean time Robert takes to complete the puzzle.\\
\hfill \mbox{\textit{Edexcel S3 2007 Q3 [7]}}