| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Non-parametric tests |
| Type | Sampling method comparison |
| Difficulty | Moderate -0.8 This is a straightforward sampling methods question requiring recall of definitions and basic calculations. Part (a) needs recognition that stratified sampling requires whole numbers (30 fish split proportionally gives non-integers), parts (b)-(c) are direct recall of quota sampling properties, and part (d) involves simple proportion calculations. No problem-solving or novel insight required—purely textbook application of sampling theory. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Sampling frame within each species of fish in the lake impossible to obtain | B1 | 'You can't / it's very difficult to number all the fish' or equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Quota sampling | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Advantages: Sample can be obtained quickly / Costs are kept to a minimum / Administration of survey is easy | B1 | Correct answer to (b) required. Some detail required |
| Disadvantages: Not possible to estimate sampling errors / Process not random / Surveyor may not be able to identify species of fish easily | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Trout: \(\frac{1400}{2450} \times 30 = 17.14\), Bass: \(\frac{600}{2450} \times 30 = 7.35\), Pike: \(\frac{450}{2450} \times 30 = 5.51\) | B1B1B1 | 1st B1 any one correct calculation seen or implied; 2nd B1 all correct to at least 1 dp; 3rd B1 for 17, 7, 6 |
| Fish are caught until quota of 17 trout, 7 bass and 6 pike are reached. If a fish is caught and the species quota is full, then this is ignored. | B1 | Accept equivalent statement. Require comment on what to do with 'extra fish' |
# Question 2:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Sampling frame within each species of fish in the lake impossible to obtain | B1 | 'You can't / it's very difficult to number all the fish' or equivalent |
**(1 mark)**
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Quota sampling | B1 | |
**(1 mark)**
## Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Advantages: Sample can be obtained quickly / Costs are kept to a minimum / Administration of survey is easy | B1 | Correct answer to (b) required. Some detail required |
| Disadvantages: Not possible to estimate sampling errors / Process not random / Surveyor may not be able to identify species of fish easily | B1 | |
**(2 marks)**
## Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Trout: $\frac{1400}{2450} \times 30 = 17.14$, Bass: $\frac{600}{2450} \times 30 = 7.35$, Pike: $\frac{450}{2450} \times 30 = 5.51$ | B1B1B1 | 1st B1 any one correct calculation seen or implied; 2nd B1 all correct to at least 1 dp; 3rd B1 for 17, 7, 6 |
| Fish are caught until quota of 17 trout, 7 bass and 6 pike are reached. If a fish is caught and the species quota is full, then this is ignored. | B1 | Accept equivalent statement. Require comment on what to do with 'extra fish' |
**(4 marks)**
---2. A lake contains 3 species of fish. There are estimated to be 1400 trout, 600 bass and 450 pike in the lake. A survey of the health of the fish in the lake is carried out and a sample of 30 fish is chosen.
\begin{enumerate}[label=(\alph*)]
\item Give a reason why stratified random sampling cannot be used.
\item State an appropriate sampling method for the survey.
\item Give one advantage and one disadvantage of this sampling method.
\item Explain how this sampling method could be used to select the sample of 30 fish. You must show your working.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2012 Q2 [8]}}