| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Calculate Type I error probability |
| Difficulty | Moderate -0.3 This is a standard hypothesis testing question covering binomial distribution basics: setting up hypotheses, finding critical regions at 5% significance, and interpreting Type I errors. While it requires understanding of statistical concepts, it follows a routine textbook format with straightforward calculations (testing p=0.2 vs p>0.2 with n=10) and no novel problem-solving or complex reasoning required. |
| 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 |
Edward can correctly identify 20% of types of wild flower. He studies some books to see if he can improve how often he can correctly identify types of wild flower. He collects a random sample of 10 types of wild flower in order to test whether or not he has improved.
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item Write suitable hypotheses for this test.
\item State a suitable test statistic that he could use. [2]
\end{enumerate}
\item Using a 5% level of significance, find the critical region for this test. [3]
\item State the probability of a Type I error for this test and explain what it means in this context. [2]
\item Edward correctly identifies 4 of the 10 types of wild flower he collected.
What conclusion should Edward reach? [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2018 Q04 [9]}}