Methods of samplingEdexcel International A Level Further Maths: Subtopic test

1. 1
   A college has 840 students, listed alphabetically on a register. The principal wants the views of 60 of them on a proposed new timetable.

   (a)

   Which of the following is the sampling frame for this survey?

   [1 mark]

   • AThe 60 students whose views are collected
   • BThe register of the 840 students
   • CThe students' opinions of the timetable
   • DThe students who are present on the day of the survey

   (b)

   A systematic sample of 60 students is taken from the register. What is the sampling interval?

   [1 mark]

   • A$780$
   • B$60$
   • C$14$
   • D$12$

   (c)

   Describe how the principal could select the systematic sample of 60 students from the register.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A council has 500 houses, numbered 001 to 500. A researcher uses a calculator to generate three-digit random numbers, in this order: 417, 862, 093, 417, 250, 501, 338, and so on. She wants to choose a simple random sample of 40 houses.

   (a)

   The random numbers are used in the order given, ignoring any number that does not match a house and any repeat. How many different houses have been selected after the first seven numbers?

   [1 mark]

   • A$4$
   • B$5$
   • C$6$
   • D$7$

   (b)

   Which statement must be true of a simple random sample of 40 houses from the 500?

   [1 mark]

   • AHouses are selected at regular intervals from the list
   • BEvery street in the council area is represented
   • CThe sample is made up of volunteers who return a questionnaire
   • DEvery possible sample of 40 houses is equally likely to be chosen

   (c)

   Explain why the numbers 862 and 501 are ignored, and why the second 417 is also ignored.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A company has 480 employees: 192 work in production, 168 in sales and 120 in administration. The managers expect views on a new working-hours policy to differ between the departments. A stratified sample of 40 employees is to be taken.

   (a)

   Calculate the number of employees that should be sampled from each department.

   [3 marks]

   (b)

   Explain why a stratified sample is more suitable than a simple random sample for this survey, state one disadvantage of stratified sampling, and state how the 16 production employees should be chosen.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A market research company wants opinions on a new brand of coffee from the adults of a town. An interviewer stands in the town's shopping centre on a Saturday morning and interviews shoppers, until she has filled quotas for age group and gender that match the make-up of the town's adult population. A manager proposes instead a systematic sample of 400 names from the town's electoral register, which lists 48 000 adults alphabetically by surname.

   (a)

   Describe how the quota sample is taken, and evaluate its use for this survey by giving two advantages and two disadvantages.

   [6 marks]

   (b)

   (i) Find the sampling interval for the manager's systematic sample and describe how the sample would be selected.
   (ii) Evaluate the manager's proposal against the quota sample, and recommend which method the company should use.

   [6 marks]

   Total for question 4: 12 marks

End of questions