A sample comprising 500 members is required from a population comprising 5000 members. It is known that the population falls into three categories made up of: 1500 members in Category A; 3000 members in Category B; and 500 members in Category C. Explain clearly how you would extract a stratified sample of the required size?
To extract a stratified sample from a population, you would need to follow these steps:
1. Identify the Categories: Determine the categories in the population based on certain characteristics or attributes. In this case, we have three categories: Category A, Category B, and Category C.
2. Determine the Sample Size: Calculate the proportion of the sample that should be assigned to each category. In this example, the sample size is 500, and the proportional sizes for each category can be calculated as follows:
- Category A: (1500/5000) * 500 = 150
- Category B: (3000/5000) * 500 = 300
- Category C: (500/5000) * 500 = 50
3. Randomly Select Samples from Each Category: Randomly select the required number of samples from each category. To do this, you can use a random number generator or a sampling method such as systematic, cluster, or stratified random sampling.
For example, to select samples from Category A (150 samples):
- Assign a number to each member of Category A from 1 to 1500.
- Use a random number generator to select 150 numbers between 1 and 1500.
- Select the corresponding members from Category A as your sample.
Repeat this process for Category B (300 samples) and Category C (50 samples).
By following these steps, you will obtain a stratified sample that accurately represents the population based on the proportions of each category.