A sixth-form college has 312 Year 12 students, 276 Year 13 students and 62 staff. The principal wants the views of a sample of 50 people from the college.
(a)
A stratified sample of 50 is taken by group. Calculate the number of people from each group in the sample.
(2 marks)
(b)
Describe how the Year 13 students in the sample should be selected.
(2 marks)
(c)
Give one reason why a stratified sample is more suitable here than a simple random sample of 50 people.
(1 mark)
3 marksCore techniqueS1.1
An online shop has a list of 450 customers who bought something last month, in the order they first registered. The manager wants a systematic sample of 30 customers.
(a)
Describe how the manager should take the systematic sample.
(2 marks)
(b)
Explain why this systematic sample is not a simple random sample.
(1 mark)
5 marksUnfamiliar problemS1.1, OT3.5
A researcher wants to estimate the mean daily screen time of 16 to 18-year-olds in a city with 14 sixth-form colleges. She stands outside the gate of one college at 4 pm on a Friday and asks the first 50 students who leave how many hours they spent on screens the previous day.
(a)
State the name of this sampling method.
(1 mark)
(b)
Give two reasons, in context, why the sample may not represent the population.
(2 marks)
(c)
Suggest how the researcher could refine her method to give a more representative sample, and describe how it would be carried out.
(2 marks)
4 marksUnfamiliar problemS1.1, S2.4
Priya wants to estimate the mean daily maximum gust at Leuchars in 2015 using the large data set, which records 184 days from May to October. She uses the first 10 days of May.
(a)
Explain why Priya's sample is likely to be biased.
(1 mark)
(b)
Describe how Priya could take a simple random sample of 10 days instead.
(2 marks)
(c)
Priya says her answer estimates the mean daily maximum gust at Leuchars for the whole of 2015. Comment on this claim.
(1 mark)
4 marksUnfamiliar problemS1.1
A college has 180 first-year and 120 second-year students. A sample of 30 is required.
(a)
Find the allocation for a proportional stratified sample.
(2 marks)
(b)
Describe how to select the students within each stratum without replacement.
(2 marks)
4 marksUnfamiliar problemS1.1
A college has 240 first-year and 160 second-year students. A sample of 40 is required.
(a)
Find the allocation for a proportional stratified sample.
(2 marks)
(b)
Describe how to select the students within each stratum without replacement.
(2 marks)
3 marksUnfamiliar problemS1.1
A list contains 300 households. A systematic sample of 30 households is taken. The random start is 7.
(a)
Find the interval and the last selected label.
(2 marks)
(b)
The list repeats a ten-household street pattern. Explain a possible weakness.
(1 mark)
3 marksUnfamiliar problemS1.1
A list contains 400 households. A systematic sample of 40 households is taken. The random start is 7.
(a)
Find the interval and the last selected label.
(2 marks)
(b)
The list repeats a ten-household street pattern. Explain a possible weakness.
(1 mark)
4 marksUnfamiliar problemS1.1
A researcher asks the first 30 people leaving a gym about weekly exercise. The target population is all adults in the town.
(a)
Identify the sampling method and explain one likely source of bias.
(2 marks)
(b)
Describe a more representative sampling design using a complete adult-resident list.
(2 marks)
4 marksUnfamiliar problemS1.1
A researcher asks the first 40 people leaving a gym about weekly exercise. The target population is all adults in the town.
(a)
Identify the sampling method and explain one likely source of bias.
(2 marks)
(b)
Describe a more representative sampling design using a complete adult-resident list.