| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2024 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed test critical region |
| Difficulty | Standard +0.3 This is a standard hypothesis testing question for a binomial proportion at A-level. It requires routine application of hypothesis test procedures (stating hypotheses, finding critical regions, conducting the test) and understanding Type I/II errors. The calculations are straightforward with tables, and the concepts are core S1/S2 material 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 |
A company produces sweets of varying colours. The company claims that the proportion of blue sweets is 13·6%. A consumer believes that the true proportion is less than this. In order to test this belief, the consumer collects a random sample of 80 sweets.
\begin{enumerate}[label=(\alph*)]
\item State suitable hypotheses for the test. [1]
\item \begin{enumerate}[label=(\roman*)]
\item Determine the critical region if the test is to be carried out at a significance level as close as possible to, but not exceeding, 5%.
\item Given that there are 6 blue sweets in the sample of 80, complete the significance test. [5]
\end{enumerate}
\item Suppose the proportion of blue sweets claimed by the company is correct. The consumer conducts the sampling and testing process on a further 20 occasions, using the sample size of 80 each time. What is the expected number of these occasions on which the consumer would reach the incorrect conclusion? [2]
\item Now suppose that the proportion of blue sweets is 7%. Find the probability of a Type II error. Interpret your answer in context. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2024 Q4 [11]}}