A sample of comprising 150 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 sample size.
To extract a stratified sample from the population, you would need to follow these steps:
1. Determine the sample size: In this case, the required sample size is 150.
2. Understand the population categories: Identify the three categories within the population - A, B, and C - with population sizes of 1500, 3000, and 500 members, respectively.
3. Calculate the sampling proportion for each category: Calculate the proportion of each category in relation to the total population. To do this, divide the population of each category by the total population size:
- Proportion of Category A = 1500 / 5000 = 0.3 or 30%
- Proportion of Category B = 3000 / 5000 = 0.6 or 60%
- Proportion of Category C = 500 / 5000 = 0.1 or 10%
4. Determine the sample size for each category: Multiply the sampling proportion of each category by the required sample size:
- Sample size for Category A = 0.3 x 150 = 45
- Sample size for Category B = 0.6 x 150 = 90
- Sample size for Category C = 0.1 x 150 = 15
5. Randomly select individuals from each category: Use a random sampling method to select the specified number of individuals from each category. Make sure the selection is representative and unbiased.
For example, to get a stratified sample:
- Randomly select 45 individuals from Category A.
- Randomly select 90 individuals from Category B.
- Randomly select 15 individuals from Category C.
By following these steps, you ensure that the sample is representative of the population's distribution across the three categories.