| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2005 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Critique of sampling methods |
| Difficulty | Easy -1.8 This is a basic conceptual question about sampling methods requiring only straightforward recall of why alphabetical sampling isn't random and knowledge of simple random sampling techniques. No calculations, mathematical reasoning, or problem-solving required—just stating textbook definitions of sampling bias and standard methods. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Method is biased because many pupils cannot be chosen | B1 | "Biased" or equivalent stated, allow "not random" |
| Allocate a number to each pupil | B1 | |
| Select using random numbers | B1 2 | State "list numbered"; Use random numbers [not "hat"] |
| (ii) \(20 - 25 = \Phi^{-1}(0.25) = -0.674\) | M1 | Standardise and equate to \(\Phi^{-1}\) [not .7754 or .5987] |
| \(\sigma = 0.674 = 7.42\) | B1 | |
| M1 | \(z\) in range [-0.675, -0.674], allow \(\pm\) | |
| A1 4 | \((\pm) 5 + z\)-value [not Φ(2) or 0.75] | |
| Answer in range [7.41, 7.42], no sign digits [SR: \(\sigma^2\): M1B1M0A0; cc: M1B1M1A0] |
**(i)** Method is biased because many pupils cannot be chosen | B1 | "Biased" or equivalent stated, allow "not random"
Allocate a number to each pupil | B1 |
Select using random numbers | B1 2 | State "list numbered"; Use random numbers [not "hat"]
**(ii)** $20 - 25 = \Phi^{-1}(0.25) = -0.674$ | M1 | Standardise and equate to $\Phi^{-1}$ [not .7754 or .5987]
$\sigma = 0.674 = 7.42$ | B1 |
| M1 | $z$ in range [-0.675, -0.674], allow $\pm$
| A1 4 | $(\pm) 5 + z$-value [not Φ(2) or 0.75]
| | Answer in range [7.41, 7.42], no sign digits [SR: $\sigma^2$: M1B1M0A0; cc: M1B1M1A0]1 It is desired to obtain a random sample of 15 pupils from a large school. One pupil suggests listing all the pupils in the school in alphabetical order and choosing the first 15 names on the list.\\
(i) Explain why this method is unsatisfactory.\\
(ii) Suggest a better method.
\hfill \mbox{\textit{OCR S2 2005 Q1 [4]}}