| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 17 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of binomial distributions |
| Type | Multiple binomial probability calculations |
| Difficulty | Moderate -0.3 This is a straightforward S1 hypothesis testing question covering standard binomial calculations and a one-tailed test. Part (i) involves direct application of binomial probability formulas and expectation (routine recall), while parts (ii)-(iv) follow a standard hypothesis testing template with clear context. The critical region calculation at 5% is mechanical, and the conclusion requires simple comparison. Slightly easier than average due to its predictable structure and lack of conceptual subtlety. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail |
6 It is known that $25 \%$ of students in a particular city are smokers. A random sample of 20 of the students is selected.
\begin{enumerate}[label=(\roman*)]
\item (A) Find the probability that there are exactly 4 smokers in the sample.\\
(B) Find the probability that there are at least 3 but no more than 6 smokers in the sample.\\
(C) Write down the expected number of smokers in the sample.
A new health education programme is introduced. This programme aims to reduce the percentage of students in this city who are smokers. After the programme has been running for a year, it is decided to carry out a hypothesis test to assess the effectiveness of the programme. A random sample of 20 students is selected.
\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 3 smokers in the sample. Complete the test, stating your conclusion clearly.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2012 Q6 [17]}}