| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2007 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | State test assumptions or distributions |
| Difficulty | Easy -1.8 This is a pure recall question asking students to name the binomial distribution and state its assumptions (independence and fixed probability). No calculation or problem-solving is required—just memorization of standard definitions from the specification. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.05b Hypothesis test for binomial proportion |
| Answer | Marks | Guidance |
|---|---|---|
| Binomial | B1 | Binomial stated or implied |
| Each element equally likely | B1 | All elements, or selections, equally likely stated |
| Choices independent | B1 | Choices independent [not just "independent"] [can get B2 even if (i) is wrong] |
Binomial | B1 | Binomial stated or implied
Each element equally likely | B1 | All elements, or selections, equally likely stated
Choices independent | B1 | Choices independent [not just "independent"] [can get B2 even if (i) is wrong]3 The proportion of adults in a large village who support a proposal to build a bypass is denoted by $p$. A random sample of size 20 is selected from the adults in the village, and the members of the sample are asked whether or not they support the proposal.\\
(i) Name the probability distribution that would be used in a hypothesis test for the value of $p$.\\
(ii) State the properties of a random sample that explain why the distribution in part (i) is likely to be a good model.\\
$4 X$ is a continuous random variable.\\
\hfill \mbox{\textit{OCR S2 2007 Q3 [3]}}