| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Calculate Type II error probability |
| Difficulty | Standard +0.3 This is a standard hypothesis testing question covering routine A-level statistics concepts: stating hypotheses, finding significance levels using binomial distribution, calculating Type II error probability, and explaining test improvements. While it requires multiple steps and understanding of error types, all techniques are textbook applications with no novel problem-solving required, 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 |
Dewi, a candidate in an election, believes that 45% of the electorate intend to vote for him. His agent, however, believes that the support for him is less than this. Given that $p$ denotes the proportion of the electorate intending to vote for Dewi,
\begin{enumerate}[label=(\alph*)]
\item state hypotheses to be used to resolve this difference of opinion. [1]
\end{enumerate}
They decide to question a random sample of 60 electors. They define the critical region to be $X \leq 20$, where $X$ denotes the number in the sample intending to vote for Dewi.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item \begin{enumerate}[label=(\roman*)]
\item Determine the significance level of this critical region.
\item If in fact $p$ is actually 0.35, calculate the probability of a Type II error.
\item Explain in context the meaning of a Type II error.
\item Explain briefly why this test is unsatisfactory. How could it be improved while keeping approximately the same significance level? [8]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 Q2 [9]}}