| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Two-tailed test critical region |
| Difficulty | Standard +0.3 This is a standard S2 hypothesis testing question requiring students to find critical regions for a binomial test using tables, state the actual significance level, and make a conclusion. While it involves multiple steps and careful probability calculations, it follows a routine procedure taught explicitly in S2 with no novel problem-solving required. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02d Binomial: mean np and variance np(1-p)5.05b Unbiased estimates: of population mean and variance5.05c Hypothesis test: normal distribution for population mean |
4. Past records suggest that $30 \%$ of customers who buy baked beans from a large supermarket buy them in single tins. A new manager questions whether or not there has been a change in the proportion of customers who buy baked beans in single tins. A random sample of 20 customers who had bought baked beans was taken.
\begin{enumerate}[label=(\alph*)]
\item Using a $10 \%$ level of significance, find the critical region for a two-tailed test to answer the manager's question. You should state the probability of rejection in each tail which should be less than 0.05 .
\item Write down the actual significance level of a test based on your critical region from part (a).
The manager found that 11 customers from the sample of 20 had bought baked beans in single tins.
\item Comment on this finding in the light of your critical region found in part (a).
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2009 Q4 [8]}}