Question 1Easy6 marks
A leisure centre manager wants to find out how often adults in a town exercise. The manager asks the first 50 adults who enter the leisure centre on a Monday morning.
(a) State the name of this sampling method.[1]
(b) Give two reasons why this sample is likely to be biased.[2]
(c) The town has 12 000 adults, of whom 7200 are under 50 years old. The manager decides instead to take a sample of 60 adults, stratified by age group (under 50, and 50 or over).
Find how many of the sample should be under 50, and describe how the manager could choose them.[3]
Find how many of the sample should be under 50, and describe how the manager could choose them.[3]
Show the answer and mark scheme
(a) Answer: Opportunity (convenience) sampling
- B1 for opportunity (or convenience) sampling
Worked solution: The manager uses the people who happen to be available: this is opportunity (convenience) sampling.
(b) Answer: People entering a leisure centre are likely to exercise more than a typical adult; people at work on a Monday morning are excluded (so some age or employment groups are under-represented).
- B1 for the sample consists of leisure-centre users, who probably exercise more often than adults in general
- B1 for a second reason, e.g. a Monday morning excludes most people who work (the sample over-represents retired or unemployed people), or everyone was sampled at one time and place
Worked solution: Adults entering a leisure centre are more likely than average to exercise regularly, and on a Monday morning most working adults are at work, so the sample is not representative of all adults in the town.
(c) Answer: 36; number a list of the adults under 50 (e.g. from the electoral register) and choose 36 using random numbers.
- M1 for \(\frac{7200}{12\,000} \times 60\)
- A1 for 36
- B1 for a description of simple random sampling within the stratum: obtain a list (sampling frame) of adults under 50, number them, and use random numbers to select 36 (ignoring repeats)
Worked solution: \(\frac{7200}{12\,000} \times 60 = 36\) of the sample should be under 50.
Using a list of all adults under 50 in the town (such as the electoral register with dates of birth), number them 1 to 7200 and use a random number generator to choose 36 different numbers.