| Exam Board | Edexcel |
|---|---|
| Module | S4 (Statistics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Type I/II errors and power of test |
| Type | Simultaneous critical region and Type II error |
| Difficulty | Standard +0.3 This S4 question tests standard definitions (size, power) and routine calculations with binomial distributions. Parts (a)-(b) are pure recall, part (c) is a standard critical region calculation, part (d) involves straightforward binomial probability calculations for Type II error and power, and part (e) requires knowledge of factors affecting power. While it requires understanding of hypothesis testing concepts and careful binomial calculations, all components are textbook exercises with no novel problem-solving required. Slightly easier than average due to the structured, formulaic nature. |
| 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 |
Define, in terms of H$_0$ and/or H$_1$,
\begin{enumerate}[label=(\alph*)]
\item the size of a hypothesis test,
[1]
\item the power of a hypothesis test.
[1]
\end{enumerate}
The probability of getting a head when a coin is tossed is denoted by $p$.
This coin is tossed 12 times in order to test the hypotheses H$_0$: $p = 0.5$ against H$_1$: $p \neq 0.5$, using a 5\% level of significance.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item Find the largest critical region for this test, such that the probability in each tail is less than 2.5\%.
[4]
\item Given that $p = 0.4$
\begin{enumerate}[label=(\roman*)]
\item find the probability of a type II error when using this test,
\item find the power of this test.
\end{enumerate}
[4]
\item Suggest two ways in which the power of the test can be increased.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S4 Q3 [12]}}