| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Multiple binomial probability calculations |
| Difficulty | Standard +0.3 This is a straightforward binomial hypothesis testing question covering standard S1 content. Part (i) involves routine binomial probability calculations and expectation. Parts (ii)-(iv) follow a textbook one-tailed test procedure with clear guidance. The calculations are mechanical with n=18, and the question explicitly prompts each step, requiring no novel insight beyond applying the standard hypothesis testing framework. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05a Hypothesis testing language: null, alternative, p-value, significance2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
1 A manufacturer produces tiles. On average 10\% of the tiles produced are faulty. Faulty tiles occur randomly and independently.
A random sample of 18 tiles is selected.
\begin{enumerate}[label=(\roman*)]
\item (A) Find the probability that there are exactly 2 faulty tiles in the sample.\\
(B) Find the probability that there are more than 2 faulty tiles in the sample.\\
(C) Find the expected number of faulty tiles in the sample.
A cheaper way of producing the tiles is introduced. The manufacturer believes that this may increase the proportion of faulty tiles. In order to check this, a random sample of 18 tiles produced using the cheaper process is selected and a hypothesis test is carried out.
\item (A) Write down suitable null and alternative hypotheses for the test.\\
(B) Explain why the alternative hypothesis has the form that it does.
\item Find the critical region for the test at the $5 \%$ level, showing all of your calculations.
\item In fact there are 4 faulty tiles in the sample. Complete the test, stating your conclusion clearly.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q1 [18]}}