| Exam Board | OCR |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2009 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modelling and Hypothesis Testing |
| Type | Confidence intervals for proportions |
| Difficulty | Standard +0.3 This is a standard two-proportion hypothesis test requiring calculation of pooled proportion, test statistic, and p-value interpretation. Part (i) is routine application of the formula, while part (ii) requires finding the critical p-value, which is slightly beyond basic recall but still a well-practiced S3 technique with no novel insight required. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean |
4 In order to compare the difficulty of two Su Doku puzzles, two random samples of 40 fans were selected. One sample was given Puzzle 1 and the other sample was given Puzzle 2. Of those given Puzzle 1, 24 could solve it within ten minutes. Of those given Puzzle 2, 15 could solve it within ten minutes.\\
(i) Using proportions, test at the $5 \%$ significance level whether there is a difference in the standard of difficulty of the two puzzles.\\
(ii) The setter believed that Puzzle 2 was more difficult than Puzzle 1. Obtain the smallest significance level at which this belief is supported.
\hfill \mbox{\textit{OCR S3 2009 Q4 [10]}}