S2 June 2010 Q1
1. Explain what you understand by
A researcher took a sample of 100 voters from a certain town and asked them who they would vote for in an election. The proportion who said they would vote for Dr Smith was 35%.
| Scheme | Marks |
|---|---|
| A population is collection of all items | B1 |
| (1) |
Notes
B1 – collection/group all items – need to have /imply all eg entire/complete/every
| Scheme | Marks |
|---|---|
| (A random variable) that is a function of the sample which contains no unknown quantities/parameters. | B1 |
| (1) |
Notes
B1 – needs function/calculation(o.e.) of the sample/random variables/observations and no unknown quantities/parameters(o.e.) NB do not allow unknown variables
e.g. “A calculation based solely on observations from a given sample.” B1
“A calculation based only on known data from a sample” B1
“A calculation based on known observations from a sample” B0
Solely/only imply no unknown quantities
| Scheme | Marks |
|---|---|
| The voters in the town | B1 |
| Percentage/proportion voting for Dr Smith | B1 |
| (2) |
Notes
B1 – Voters
Do not allow 100 voters.
B1 – percentage/ proportion voting (for Dr Smith)
the number of people voting (for Dr Smith)
Allow 35% of people voting (for Dr Smith)
Allow 35 people voting (for Dr Smith)
Do not allow 35% or 35 alone
| Scheme | Marks |
|---|---|
| Probability Distribution of those voting for Dr Smith from all possible samples (of size 100) | B1 |
| (1) | |
| (5 marks) |
Notes
B1 – answers must include all three of these features
(i) All possible samples,
(ii) their associated probabilities,
(iii) context of voting for Dr Smith.
e.g “It is all possible values of the percentage and their associated probabilities.” B0 no context