| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Critique given sampling method |
| Difficulty | Easy -1.2 This is a straightforward S3 sampling methods question requiring only recall of standard bias sources, definitions of systematic/stratified sampling, and basic use of random number tables. No calculations beyond simple arithmetic (stratification proportions) or problem-solving insight needed—purely textbook application of sampling terminology and procedures. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| (Allow "not a representative sample" in place of "not a random sample") | B1g, B1h | (2 marks) |
| Answer | Marks |
|---|---|
| Label employees (1-550) or obtain an ordered list | B1 |
| Select first using random numbers (from 1 - 11) | B1 |
| Then select every 11th person from the list | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Label managers (1-55) and cleaners (1-495) | M1 | |
| Use random numbers to select... | M1 | |
| ...\(5\) managers and \(45\) cleaners | A1 | (6 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| 390, 372 (They must be in this order) | B1, B1 | (2 marks) |
**Part (a)**
Only cleaners - no managers i.e. not all types. OR Not a random sample
1st 50 may be in same shift/group/share same views. OR Not a random sample
(Allow "not a representative sample" in place of "not a random sample") | B1g, B1h | (2 marks)
**Part (b)(i)**
Label employees (1-550) or obtain an ordered list | B1 |
Select first using random numbers (from 1 - 11) | B1 |
Then select every 11th person from the list | B1 |
**Part (b)(ii)**
Label managers (1-55) and cleaners (1-495) | M1 |
Use random numbers to select... | M1 |
...$5$ managers and $45$ cleaners | A1 | (6 marks)
**Part (c)**
390, 372 (They must be in this order) | B1, B1 | (2 marks)
**Guidance Notes:**
After 1st B1, comments should be in context, i.e. mention cleaners, managers, types of worker etc
1st B1g for one row
2nd B1h for both rows. "Not a random sample" only counts once.
Score B1B0 or B1B1 or B0B0 on EPEN
(b)(i) 1st B1 for idea of labelling or getting an ordered list. No need to see 1-550.
2nd B1 selecting first member of sample using random numbers (1-11 need not be mentioned)
3rd B1 selecting every $nth$ where $n = 11$.
(ii) 1st M1 for idea of two groups and labelling both groups. (Actual numbers used not required)
2nd M1 for use of random numbers within each strata. Don't give for SRS from all 550.
"Assign random numbers to managers and cleaners" scores M0M1
A1 for 5 managers and 45 cleaners. (This mark is dependent upon scoring at least one M)
---\begin{enumerate}
\item A researcher is hired by a cleaning company to survey the opinions of employees on a proposed pension scheme. The company employs 55 managers and 495 cleaners.
\end{enumerate}
To collect data the researcher decides to give a questionnaire to the first 50 cleaners to leave at the end of the day.\\
(a) Give 2 reasons why this method is likely to produce biased results.\\
(b) Explain briefly how the researcher could select a sample of 50 employees using\\
(i) a systematic sample,\\
(ii) a stratified sample.
Using the random number tables in the formulae book, and starting with the top left hand corner (8) and working across, 50 random numbers between 1 and 550 inclusive were selected. The first two suitable numbers are 384 and 100 .\\
(c) Find the next two suitable numbers.
\hfill \mbox{\textit{Edexcel S3 2008 Q5 [10]}}