Statistical Sampling
1. This question has 3 part(s).
1.1. Ramona wants to examine data about the number of people who work from home. As there are 10 regions in the large data set, she initially decides to look at a sample of 10 Local Authorities. She decides to compare data from the first Local Authority listed for each region, with the results shown in the table below:
Region | Local Authority | Work mainly at or from home |
North East | County Durham | 20 652 |
North West | Allerdale | 6025 |
Yorkshire & The Humber | Barnsley | 7945 |
East Midlands | Amber Valley | 5697 |
West Midlands | Birmingham | 32 837 |
East of England | Babergh | 5776 |
London | Barking & Dagenham | 4740 |
South East | Adur | 2991 |
South West | Bath & North East Somerset | 10 624 |
Wales | Anglesey | 4026 |
The North East is made up of just 12 Local Authorities whereas the South East contains 67 Local Authorities. All other regions have between 21 and 47 Local Authorities each.
Give one reason for why the sample above is not a stratified sample.
1.2. Explain why a sample size of 10 would not be suitable if Ramona decided to use a stratified sample for her study.
1.3. Suggest a way Ramona could fix the problem outlined in part (b) in order to create a stratified sample. You must justify your suggestion with mathematical working.
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