| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Calculate Type II error probability |
| Difficulty | Moderate -0.3 This is a straightforward hypothesis testing question covering standard concepts (null/alternative hypotheses, Type I/II errors) with routine binomial probability calculations. The computations are direct applications of B(10, 1/6) and B(10, 1/3) with no conceptual challenges, making it slightly easier than average for A-level statistics. |
| Spec | 2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion |
Jeevan thinks that a six-sided die is biased in favour of six. In order to test this, Jeevan throws the die 10 times. If the die shows a six on at least 4 throws out of 10, she will conclude that she is correct.
\begin{enumerate}[label=(\roman*)]
\item State appropriate null and alternative hypotheses. [1]
\item Calculate the probability of a Type I error. [3]
\item Explain what is meant by a Type II error in this situation. [1]
\item If the die is actually biased so that the probability of throwing a six is $\frac{1}{3}$, calculate the probability of a Type II error. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2011 Q6 [8]}}