WJEC Maths for AS: Applied sample

1 Statistical sampling 14 Test yourself ➊ Amy read in a local newspaper that the average number of hours per day of sunshine in her area in June is 8. She decides to test this by recording the number of hours of sunshine per day for the week beginning 1st June 2017. (a) Comment of the suitability of this sample to test the newspaper’s claim. (b) How might Amy obtain more representative data in order to test the claim? ➋ A popular club has a maximum capacity of 300 and is full to capacity every Saturday. A study of the people entering the club needs to be carried out and a sample size of 30 is to be used. (a) Describe how systematic sampling could be used to obtain the sample. (b) One person suggests that random sampling could be used with each person being given a number as they come into the club and then the 30 numbers are picked at random. Explain why this method of sampling would be difϐicult in this situation. ➌ Julie thinks that everyone watches one or more soaps. She decides to test this by asking all her friends. (a) Give the name of the sampling method she has used. (b) Explain why her sample is likely to be biased. ➍ A company is researching the education levels of its employees. Each employee is allocated a number and a random number generator is used to select people to interview. Give the name of this sampling technique. ➎ The houses along a road called High Street are numbered from 1 to 350. The local council are going to undertake a survey about local amenities and they need a sample using 50 households. (a) Explain using the information above, the difference between the population and a sample. (b) Give two reasons why the council has decided to take a sample rather than use the population for the survey. (c) Explain how they might choose an unbiased sample. ➏ A football ground has a maximum capacity of 40 000 supporters. A brief survey is to be conducted about the facilities at the ground. At the next match a sample of 50 supporters is to be used for the survey. (a) Explain what the population would be. (b) Give two reasons why a sample is used rather than the population for the survey. (c) The people who are in charge of conducting the survey want to complete the survey quickly so they decide to do the survey on the ϐirst 50 supporters entering the ground. (i) Give the name of this sampling technique. (ii) Explain why this sampling technique might not represent the population.