| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2026 |
| Session | January |
| Marks | 6 |
| Topic | Hypothesis test of binomial distributions |
| Type | Two-tailed test critical region |
| Difficulty | Moderate -0.3 This is a straightforward application of binomial hypothesis testing with standard procedures: stating hypotheses, finding critical regions using tables at 5% significance, and interpreting results. While it requires multiple steps and careful probability calculations for a two-tailed test, it follows a routine textbook template with no novel problem-solving or conceptual challenges beyond standard A-level Statistics content. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
5.
The proportion of left-handed adults in a country is 10\%\\
Freya believes that the proportion of left-handed adults under the age of 25 in this country is different from 10\%\\
She takes a random sample of 40 adults under the age of 25 from this country to investigate her belief.
\begin{enumerate}[label=(\alph*)]
\item Find the critical region for a suitable test to assess Freya's belief.
You should
\begin{itemize}
\item state your hypotheses clearly
\item use a $5 \%$ level of significance
\item state the probability of rejection in each tail
\item Given the null hypothesis is true what is the probability of it being rejected in part (a)?
\end{itemize}
In Freya's sample 7 adults were left-handed.
\item With reference to your answer in part (a) comment on Freya's belief.
\section*{6.}
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2026 Q5 [6]}}