S3 June 2013 Q3
3. A college manager wants to survey students’ opinions of enrichment activities.
She decides to survey the students on the courses summarised in the table below.
| Course | Number of students enrolled |
|---|---|
| Leisure and Sport | 420 |
| Information Technology | 337 |
| Health and Social Care | 200 |
| Media Studies | 43 |
Each student takes only one course.
The manager has access to the college’s information system that holds full details of each of the enrolled students including name, address, telephone number and their course of study. She wants to compare the opinions of students on each course and has a generous budget to pay for the cost of the survey.
The manager decides to take a stratified sample of 100 students.
| Scheme | Marks |
|---|---|
| (i) Quota Sampling: e.g. Advantages: Fieldwork can be done quickly, or administering the test is easy, or costs are kept to a minimum (cheap), or gives estimates for each course. or OK for large populations or sampling frame not required (o.e.) e.g. Disadvantages: Non-random process or not possible to estimate the sampling errors, or non response not recorded, or interviewer can introduce bias in sample choice. (o.e.) | B1 |
| (ii) Stratified Sampling: e.g. Advantages: Can give accurate estimates as it is a random process, or gives estimates for each course or representative of [BUT not “proportional” to] the whole population. (o.e.) e.g. Disadvantages: Sampling frame required, or strata may not be clear as some students overlap courses or not suitable for large populations. (o.e.) | B1 |
| (2) |
Notes
Do not penalise for lack of context in part (a)
1st B1 for an advantage and a disadvantage for quota sampling (must be 1st or labelled (i))
2nd B1 for an advantage and a disadvantage for stratified sampling (2nd or labelled (ii))
Do not allow opposite pairs e.g. “quicker/easier” for quota sampling and “takes a long time/more difficult” for stratified or quota “easy to use” but strat. “hard for large populations”
Do not allow same reason for both e.g. “gives estimates for each course”
| Scheme | Marks |
|---|---|
| Total enrolments=1000 (may be implied by calculations) | B1 |
| Leisure and Sport\(= \dfrac{420}{1000} \times 100 = 42\) | M1 |
| Information Technology\(= \dfrac{337}{1000} \times 100 = 33.7 = 34\) Health and Social Care\(= \dfrac{200}{1000} \times 100 = 20\) Media Studies\(= \dfrac{43}{1000} \times 100 = 4.3 = 4\) | A1 |
| (3) |
Notes
M1 for one correct calculation, ft their “1000”
A1 for 42, 34, 20 and 4 only
| Scheme | Marks |
|---|---|
| The college’s information system would be used to identify each student and which course they are enrolled on. i.e. idea of sampling frame or list for each course. | B1 |
| Use of random numbers to select required number of students from each course | B1 |
| (2) | |
| (7 marks) |
Notes
1st B1 for some mention of a suitable sampling frame. Need not give the specific term but a suitable source of list is required for all students in each course.
2nd B1 for mentioning use of random numbers or some random selection process for each course. If they are describing systematic sampling score B0 here