| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2008 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Compare test procedures or parameters |
| Difficulty | Standard +0.3 This is a standard two-sample binomial proportion test with straightforward application of the normal approximation. Part (i) requires routine hypothesis testing mechanics (pooled proportion, test statistic, critical value comparison). Part (ii) tests understanding of when to use pooled vs unpooled variance, which is a conceptual point but well-covered in S3 syllabi. Slightly above average due to the two-sample context and the conceptual twist in part (ii), but still a textbook exercise requiring no novel insight. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
3 A transport authority wished to compare the performance of two rail companies, Western and Northern. They noted that the number of 'on-time' arrivals for a random sample of 80 Western trains over a particular route was 71 . The corresponding number for a random sample of 90 Northern trains over a similar route was 73 .\\
(i) Test, at the $5 \%$ significance level, whether the population proportion of on-time Western trains exceeds the population proportion of on-time Northern trains.\\
(ii) Ranjit wishes to test whether the population proportion of on-time Western trains exceeds the population proportion of on-time Northern trains by more than 0.01 . What variance estimate should she use?
\hfill \mbox{\textit{OCR S3 2008 Q3 [9]}}