| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | One-tailed hypothesis test |
| Difficulty | Moderate -0.3 This is a straightforward application of normal approximation to binomial with standard hypothesis testing procedures. Part (a) requires routine calculation with continuity correction, and part (b) involves finding a critical value from tables. The setup is clear, the method is standard, and no novel insight is required—slightly easier than average due to being a textbook application. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 0.0348 | B1 (1.1) | BC 0.03482475. Allow if seen correct to at least 3 sf. We do not want to penalize wrong rounding too often |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(X \leq 4) = 0.013(337876...)\) or \(P(X \leq 3) = 0.004(09062...)\) found | M1 (3.1a) | Accept \(P(X \leq 4) > 0.01\) or \(P(X \leq 3) < 0.01\) |
| Hence 4 is not in CR, or 3 is in CR | M1 (2.2a) | Allow M1 for one (correct) of these |
| so CR is \(\{0,1,2,3\}\) or \(X \leq 3\) | A1 (3.2a) | Both probabilities must be correct |
| [3] |
## Question 4(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 0.0348 | B1 (1.1) | BC 0.03482475. Allow if seen correct to at least 3 sf. We do not want to penalize wrong rounding too often |
| **[1]** | | |
---
## Question 4(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(X \leq 4) = 0.013(337876...)$ or $P(X \leq 3) = 0.004(09062...)$ found | M1 (3.1a) | Accept $P(X \leq 4) > 0.01$ or $P(X \leq 3) < 0.01$ |
| Hence 4 is not in CR, or 3 is in CR | M1 (2.2a) | Allow M1 for one (correct) of these |
| so CR is $\{0,1,2,3\}$ or $X \leq 3$ | A1 (3.2a) | Both probabilities must be correct |
| **[3]** | | |
---4 In a certain country it is known that 11\% of people are left-handed.
\begin{enumerate}[label=(\alph*)]
\item Calculate the probability that, in a random sample of 98 people from this country, 5 or fewer are found to be left-handed, giving your answer correct to 3 significant figures.
An anthropologist believes that the proportion of left-handed people is lower in a particular ethnic group.
The anthropologist collects a random sample of 98 people from this particular ethnic group in order to test the hypothesis that the proportion of left-handed people is less than $11 \%$.
The anthropologist carries out the test at the $1 \%$ level.
\item Determine the critical region for this test.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2020 Q4 [4]}}