| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Z-tests (known variance) |
| Type | One-tail z-test (lower tail) |
| Difficulty | Standard +0.3 This is a straightforward one-sample z-test with given variance, requiring standard hypothesis test procedure (stating hypotheses, calculating test statistic, comparing to critical value). Part (ii) tests understanding of when normality is needed (small sample size n=4), but both parts are routine S2 material with no problem-solving insight required. |
| Spec | 2.05c Significance levels: one-tail and two-tail2.05e Hypothesis test for normal mean: known variance |
5 Over a long period the number of visitors per week to a stately home was known to have the distribution $\mathrm { N } \left( 500,100 ^ { 2 } \right)$. After higher car parking charges were introduced, a sample of four randomly chosen weeks gave a mean number of visitors per week of 435 . You should assume that the number of visitors per week is still normally distributed with variance $100 ^ { 2 }$.\\
(i) Test, at the $10 \%$ significance level, whether there is evidence that the mean number of visitors per week has fallen.\\
(ii) Explain why it is necessary to assume that the distribution of the number of visitors per week (after the introduction of higher charges) is normal in order to carry out the test.
\hfill \mbox{\textit{OCR S2 2008 Q5 [9]}}