WJEC Maths for AS: Applied sample

1.3 Sampling techniques: simple random sampling, systematic sampling and opportunity sampling 11 Answer 1 The only way to ϐind the exact information about ϐish in the lake would be to drain the lake and collect the ϐish so that the entire population of ϐish could be analysed – this is impractical. Instead a random sample of 300 ϐish was collected using nets and the results were: Bream 46 Trout 128 Roach 126 Using this hopefully representative sample, we can make inferences about the ϐish population of the lake. Here are some inferences which could be made: • There are more trout and roach compared to bream – this is a correct inference as there are signiϐicant differences in the numbers in the sample. • The population of bream is about one third of the population of trout or roach – this is a reasonable inference. Here we are quantifying the inference (i.e. giving numeric information). • There are more trout than roach in the lake – although this is true for the sample there is not a signiϐicant difference (only 2 ϐish). If we took another random sample we could get slightly different results resulting in more roach compared to trout so this is an inference we should not make. 1.3 Sampling techniques: simple random sampling, systematic sampling and opportunity sampling There are a number of different ways a sample may be taken: • Simple random sampling – each member of the population has an equal probability of being included in the sample. Hence the members of the population to be included in the sample are picked ‘randomly’. To generate a random sample the members of the population can be given numbers and then numbered balls can be picked out of a bag or a calculator can be used. There are also websites which you can use to generate random numbers in a speciϐied range. • Systematic sampling – is where sample members are selected from a larger population according to a random starting point and a ϐixed sampling interval. The sampling interval is found by dividing the population size by the desired sample size. For example, if there is a population of 200 households in a street and a sample size of 20 is taken then you can consider all the houses from 1 to 200 arranged in a circle. You could then choose to start at a randomly picked house (say number 12) and then calculate the sampling interval ( i.e. sampling interval = population sample size = 200 20 = 10 ) so you would then survey house 12 and then 22, then 32 and so on until you go right around in the circle back to house 12. It is important not to make an inference about the population based on a small difference in the sample. Remember that different samples will have slight differences in their make-up. Active Learning There are 200 houses in a street and you want to send a survey to 50 houses. You number each address from 1 to 200 and then select a random sample of 50 numbers. You do not want any duplicate numbers. Use the following random number website to randomly pick these 50 numbers without any duplicates. www.random.org/integers Evaluate this website explaining how easy, or not, it was to carry out this task.