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.
a critical region.
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.
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.
Write down the actual significance level of the above test.
In the school holidays, 1 call occurs in a 10 minute interval.
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.
\begin{enumerate}[label=(\alph*)]
\item Explain what you understand by\\
\begin{enumerate}[label=(\roman*)]
\item a hypothesis test,
\item a critical region.
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.
\end{enumerate}
\item 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.
\item Write down the actual significance level of the above test.
In the school holidays, 1 call occurs in a 10 minute interval.
\item 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.\\
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2008 Q7 [14]}}