| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Two-tailed test setup or execution |
| Difficulty | Standard +0.8 This is a standard two-tailed Poisson hypothesis test requiring calculation of significance level from given critical regions and Type II error probability. While it involves multiple steps and careful probability calculations using Poisson tables, it follows a well-established procedure taught in S2 with no novel insight required. The computational demands and need to work with a specific alternative hypothesis elevate it slightly above average difficulty. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
3 The random variable $G$ has the distribution $\operatorname { Po } ( \lambda )$. A test is carried out of the null hypothesis $\mathrm { H } _ { 0 } : \lambda = 4.5$ against the alternative hypothesis $\mathrm { H } _ { 1 } : \lambda \neq 4.5$, based on a single observation of $G$. The critical region for the test is $G \leqslant 1$ and $G \geqslant 9$.\\
(i) Find the significance level of the test.\\
(ii) Given that $\lambda = 5.5$, calculate the probability that the test results in a Type II error.
\hfill \mbox{\textit{OCR S2 2008 Q3 [8]}}