| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of a Poisson distribution |
| Type | Two-tailed test setup or execution |
| Difficulty | Standard +0.3 This is a straightforward application of Poisson hypothesis testing with standard procedures: defining terms, finding critical regions from tables, and conducting a one-tailed test. While it requires understanding of hypothesis testing framework and Poisson distribution, all steps are routine S2 material with no novel problem-solving required. The calculations are direct table lookups rather than complex manipulations. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05c Significance levels: one-tail and two-tail5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x! |
\begin{enumerate}
\item (a) Explain what you understand by\\
(i) a hypothesis test,\\
(ii) a critical region.
\end{enumerate}
During term time, incoming calls to a school are thought to occur at a rate of 0.45 per minute. To test this, the number of calls during a random 20 minute interval, is recorded.\\
(b) Find the critical region for a two-tailed test of the hypothesis that the number of incoming calls occurs at a rate of 0.45 per 1 minute interval. The probability in each tail should be as close to $2.5 \%$ as possible.\\
(c) Write down the actual significance level of the above test.
In the school holidays, 1 call occurs in a 10 minute interval.\\
(d) Test, at the $5 \%$ level of significance, whether or not there is evidence that the rate of incoming calls is less during the school holidays than in term time.\\
\hfill \mbox{\textit{Edexcel S2 2008 Q7 [14]}}