| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | September |
| Marks | 8 |
| Topic | Z-tests (known variance) |
| Type | Two-tail z-test |
| Difficulty | Moderate -0.3 This is a straightforward application of a one-sample z-test with known variance, requiring standard hypothesis test procedure (stating hypotheses, calculating test statistic, comparing to critical value). Part (ii) tests understanding of Type I error definition, which is direct recall. The question is slightly easier than average as it's a textbook application with clear setup and no conceptual complications. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05c Significance levels: one-tail and two-tail2.05e Hypothesis test for normal mean: known variance |
12 In the past, the time spent by customers in a certain shop had mean 10.5 minutes and standard deviation 4.2 minutes. Following a change of layout in the shop, the mean time spent in the shop by a random sample of 50 customers is found to be 12.0 minutes.\\
(i) Assuming that the standard deviation is unchanged, test at the $1 \%$ significance level whether the mean time spent by customers in the shop has changed.\\
(ii) Another random sample of 50 customers is chosen and a similar test at the $1 \%$ significance level is carried out. Given that the population mean time has not changed, state the probability that the conclusion of the test will be that the population mean time has changed.
\hfill \mbox{\textit{OCR H240/02 2018 Q12 [8]}}