| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | One-tailed test critical region |
| Difficulty | Standard +0.3 This is a straightforward hypothesis testing question requiring students to find a critical value using binomial distribution tables (part a) and recognize that part (b) simply asks for the significance level itself (5%). Both parts are standard bookwork applications with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation |
A student has an ordinary six-sided dice. The student suspects that it is biased against six, so that when it is thrown, it is less likely to show a six than if it were fair.
In order to test this suspicion, the student plans to carry out a hypothesis test at the 5% significance level.
The student throws the dice 100 times and notes the number of times, $X$, that it shows a six.
\begin{enumerate}[label=(\alph*)]
\item Determine the largest value of $X$ that would provide evidence at the 5% significance level that the dice is biased against six. [3]
\end{enumerate}
Later another student carries out a similar test, at the 5% significance level. This student also throws the dice 100 times.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item It is given that the dice is fair.
Find the probability that the conclusion of the test is that there is significant evidence that the dice is biased against six. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2023 Q12 [4]}}