Practise Sampling and capture–recapture. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
Bella wants to find out how much time adults in a city spend on the internet. Bella puts a survey on a website and uses the first 100 replies.
(a) Give one reason why this sample may be biased.[1]
(b) Suggest one way in which Bella could improve the sample.[1]
Show the answer and mark scheme
(a)Answer: Only people who use the internet (and choose to reply) are included.
C1 for a correct reason, e.g. only people who use the internet (and choose to reply) are included
(b)Answer: Choose adults at random from the whole city and survey them in a way that does not need the internet.
C1 for a sensible improvement, e.g. choose adults at random from the whole city and survey them in a way that does not need the internet
Question 2Medium4 marks
Ruth wants to estimate the number of fish in a pond. She catches 40 fish, puts a tag on each one and returns them to the pond. A week later she catches 50 fish. 8 of these fish have a tag.
(a) Work out an estimate for the number of fish in the pond.[2]
(b) State one assumption that Ruth has made.[1]
(c) Some of the tags fell off before the second catch. Explain what effect this has on Ruth's estimate.[1]
Show the answer and mark scheme
(a)Answer: 250
M1 for \(\frac{40 \times 50}{8}\) or \(\frac{8}{50} = \frac{40}{N}\)
A1 for 250
Worked solution: \(\frac{8}{50} = \frac{40}{N}\), so \(N = \frac{40 \times 50}{8} = 250\).
(b)Answer: E.g. the number of fish in the pond does not change during the week.
B1 for a correct assumption, e.g. no fish are born, die, arrive or leave; the tagged fish mix evenly with the others; tags do not fall off; every fish is equally likely to be caught
Worked solution: The method assumes the population is the same size at both catches and the tagged fish are spread evenly through it.
(c)Answer: Fewer tagged fish are caught than should be, so 8 is too small and the estimate is too large (an overestimate).
C1 for explaining that fewer tagged fish are recaught, so the estimate is too high
Worked solution: Dividing by a number that is too small (fewer tagged fish recaught) makes \(\frac{40 \times 50}{8}\) too large.
Question 3Hard6 marks
A company has 600 employees: 330 office staff and 270 warehouse staff. Omar wants to estimate how many of the employees would use a staff gym. Omar asks 80 employees who are in the staff canteen at lunchtime whether they would use a staff gym. Of these 80 people, 64 are office staff and 16 are warehouse staff. 48 of the office staff and 8 of the warehouse staff say yes.
(a) Omar uses the sample to estimate the number of employees at the company who would use a staff gym. Work out Omar's estimate.[2]
(b) Show that office staff are over-represented in Omar's sample.[2]
(c) Explain why Omar's estimate is likely to be too high.[2]
(b)Answer: Office staff are 80% of the sample but only 55.00000000000001% of all the employees at the company.
M1 for \(\frac{64}{80}\) (= 80%) and \(\frac{330}{600}\) (= 55.00000000000001%) oe, or for comparing the sampling fractions \(\frac{64}{330}\) and \(\frac{16}{270}\)
C1 for a correct comparison, e.g. 80% of the sample are office staff but only 55.00000000000001% of all the employees at the company are
Worked solution: \(\frac{64}{80} = 80\%\) of the sample are office staff, but \(\frac{330}{600} = 55.00000000000001\%\) of all the employees at the company are office staff. So office staff are over-represented.
(c)Answer: A greater proportion of the office staff said yes (\(\frac{3}{4}\) compared with \(\frac{1}{2}\)), and the office staff are over-represented, so the proportion saying yes in the sample is too large.
C1 for comparing the proportions saying yes, e.g. \(\frac{48}{64}\) of the office staff but only \(\frac{8}{16}\) of the warehouse staff
C1 for linking this to the over-representation of the office staff (or to where the sample was taken, e.g. the employees in the canteen at that time may not be typical of all the employees), so the estimate is too high