| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed hypothesis test (lower tail, H₁: p < p₀) |
| Difficulty | Moderate -0.3 This is a straightforward one-tailed binomial hypothesis test with clearly stated hypotheses (H₀: p=0.14, H₁: p<0.14). Students need to calculate P(X≤2) under the null hypothesis and compare to 10% significance level. Part (ii) requires basic recall about independence assumptions. The calculations are routine and the setup is standard textbook material, making it slightly easier than average. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
4 A television company believes that the proportion of adults who watched a certain programme is 0.14 . Out of a random sample of 22 adults, it is found that 2 watched the programme.\\
(i) Carry out a significance test, at the $10 \%$ level, to determine, on the basis of this sample, whether the television company is overestimating the proportion of adults who watched the programme.\\
(ii) The sample was selected randomly. State what properties of this method of sampling are needed to justify the use of the distribution used in your test.
\hfill \mbox{\textit{OCR S2 2009 Q4 [10]}}