Population, sample and sampling techniquesEdexcel A-Level Maths: Subtopic test

1. 1
   A college has 900 students: 540 in Year 12 and 360 in Year 13. The principal wants to find out opinion on a new timetable by asking a sample of 60 students.

   (a)

   Which of the following is the population in this investigation?

   [1 mark]

   • AThe 60 students asked
   • BAll 900 students at the college
   • CThe 540 Year 12 students
   • DAll students in the town

   (b)

   The principal takes a stratified sample of 60 students using year group as the strata. How many Year 13 students are in the sample?

   [1 mark]

   • A20
   • B30
   • C24
   • D36

   (c)

   State one advantage and one disadvantage of using a sample rather than a census in this investigation.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A factory produces 2000 bottles each day, numbered 1 to 2000 in order of production. A quality controller takes a systematic sample of 80 bottles, choosing the starting bottle at random from the first interval.

   (a)

   What is the sampling interval?

   [1 mark]

   • A25
   • B80
   • C2000
   • D40

   (b)

   The first bottle selected is number 12. Which of these bottles is also in the sample?

   [1 mark]

   • A1000
   • B1250
   • C1500
   • D987

   (c)

   The bottling machine has 25 filling nozzles used in turn, and the 7th nozzle is faulty. Explain why the controller's sample may give a misleading picture of the proportion of faulty bottles.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A market researcher wants to find out how adults in a town feel about a new bus service. She stands outside the railway station on a Monday morning and interviews the first 20 men and the first 20 women who pass and agree to answer.

   (a)

   Name the sampling method used and give two reasons why the sample may not be representative of adults in the town.

   [3 marks]

   (b)

   The researcher has access to the town's electoral register of 12 000 names. Describe how she could select a simple random sample of 50 adults, and state one advantage of this over her method.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school has 900 students: 450 in Years 7 to 9, 300 in Years 10 and 11, and 150 in the sixth form. The head teacher wants to estimate the mean number of hours of sleep students get on a school night, using a sample of 60 students.

   (a)

   (i) Calculate how many students from each group should be in a stratified sample of 60.
   (ii) Explain why a stratified sample is more appropriate than asking the 30 students in her own tutor group.
   (iii) A second teacher takes another stratified sample of 60 and finds a different mean. Explain why this can happen.

   [6 marks]

   (b)

   Evaluate the use of a census, instead of a stratified sample, for this investigation, and state which you would recommend.

   [6 marks]

   Total for question 4: 12 marks

End of questions