A superstore manager wishes to give out a survey to a sample of 25 of its workers. It wants the sample to be a good representation of the workers. The table shows the numbers of workers in each section of the work force:
Working tills: 32
Stacking shelves: 24
Office/managers: 24
Warehouse: 20
Describe exactly how this can be done.
any help?
Either it can be done completely randomly or randomly within each group, taking 8 from the largest group, 5 from the smallest and 6 each from the middle groups. (That is 25% of each group.)
To create a survey sample that is a good representation of the workers in each section, we need to ensure that the proportion of workers from each section in the sample is similar to the actual proportion in the workforce.
Here's a step-by-step process to achieve this:
1. Calculate the proportion of workers in each section by dividing the number of workers in that section by the total number of workers.
Working tills proportion: 32 / (32 + 24 + 24 + 20) = 0.320
Stacking shelves proportion: 24 / (32 + 24 + 24 + 20) = 0.240
Office/managers proportion: 24 / (32 + 24 + 24 + 20) = 0.240
Warehouse proportion: 20 / (32 + 24 + 24 + 20) = 0.200
2. Multiply these proportions by the desired sample size (25) to get the target number of workers from each section in the sample.
Target number from working tills: 0.320 * 25 = 8
Target number from stacking shelves: 0.240 * 25 = 6
Target number from office/managers: 0.240 * 25 = 6
Target number from warehouse: 0.200 * 25 = 5
3. Since we can't have a fractional number of workers, we round the target numbers to the nearest whole number, while making sure that the sum of all target numbers equals the sample size.
Target number from working tills: 8 (rounded from 8.00)
Target number from stacking shelves: 6 (rounded from 6.00)
Target number from office/managers: 6 (rounded from 6.00)
Target number from warehouse: 5 (rounded from 5.00)
4. Select the required number of workers randomly from each section to create the sample.
For example, randomly select 8 workers from the working tills section, 6 workers from the stacking shelves section, 6 workers from the office/managers section, and 5 workers from the warehouse section. This would give you a sample of 25 workers that is a good representation of the workforce.
Remember to use an unbiased random sampling method, such as using a random number generator or drawing names from a hat, to ensure the sample is truly representative.