Random Sampling Statistics Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA university has 12,000 students: 7,200 undergraduates and 4,800 postgraduates. A researcher wants a stratified sample of 200 students. (a) How many undergraduates and postgraduates should be in the sample? (b) How does this compare to what might happen with a simple random sample?
Solution
- 1 Step 1: (a) Proportional allocation: Undergrad proportion = , so undergrads. Postgrad proportion = , so postgrads.
- 2 Step 2: (b) With simple random sampling, by chance the sample might have 140 undergrads and 60 postgrads, or 100 and 100. Stratified sampling guarantees the exact proportion of 120:80, ensuring both groups are properly represented.
Answer
(a) 120 undergraduates and 80 postgraduates. (b) Simple random sampling might over- or under-represent either group by chance; stratified sampling guarantees proportional representation.
Stratified sampling with proportional allocation ensures each stratum is represented in the sample in the same proportion as in the population. This reduces sampling variability and guarantees representation of important subgroups, which simple random sampling cannot guarantee.
About Random Sampling
Random sampling is a method of selecting individuals from a population where every member has an equal chance of being chosen, ensuring the sample is unbiased and representative of the whole population.
Learn more about Random Sampling →More Random Sampling Examples
Example 1 easy
A school has 500 students numbered 001–500. Describe how to select a simple random sample of 20 stud
Example 2 mediumExplain the difference between simple random sampling, stratified sampling, and systematic sampling.
Example 3 mediumA factory produces 10,000 widgets per day. A quality inspector wants to check 100 widgets. She takes