Which sampling method guarantees that every member of the population has an equal chance to be selected?

Which sampling method guarantees that every member of the population has an equal chance to be selected?

• A. Simple random sampling.
• B. Systematic sampling.
• C. Stratified sampling.
• D. Cluster sampling.

Answer: (B)

The key idea is equal probability of selection for every member of the population. Simple random sampling gives each person the same chance of being included in the sample, and every possible sample of the desired size is equally likely. For a population of size N and a sample of size n, that chance is n/N for each individual. This uniform likelihood comes from treating everyone identically and using a random mechanism to pick the sample. Systematic sampling, where you pick a random starting point and then select every k-th item, can be efficient, but it doesn’t guarantee equal probability for every person. If there’s any pattern in the listing or ordering, some individuals can end up more likely to be included than others, depending on where the random start lands. Stratified sampling seems appealing for ensuring representation across groups, but individuals’ chances depend on their stratum and how the sample is allocated among strata. Unless you set up a very specific, often impractical scheme to make every person’s overall probability equal, equal likelihood across the entire population isn’t guaranteed. Cluster sampling involves selecting entire groups (clusters) and surveying everyone inside chosen clusters. People in non-selected clusters have zero chance of being included, so equal probability across all individuals is not achieved. So the method that guarantees equal chance for every member is simple random sampling.

The key idea is equal probability of selection for every member of the population. Simple random sampling gives each person the same chance of being included in the sample, and every possible sample of the desired size is equally likely. For a population of size N and a sample of size n, that chance is n/N for each individual. This uniform likelihood comes from treating everyone identically and using a random mechanism to pick the sample.

Systematic sampling, where you pick a random starting point and then select every k-th item, can be efficient, but it doesn’t guarantee equal probability for every person. If there’s any pattern in the listing or ordering, some individuals can end up more likely to be included than others, depending on where the random start lands.

Stratified sampling seems appealing for ensuring representation across groups, but individuals’ chances depend on their stratum and how the sample is allocated among strata. Unless you set up a very specific, often impractical scheme to make every person’s overall probability equal, equal likelihood across the entire population isn’t guaranteed.

Cluster sampling involves selecting entire groups (clusters) and surveying everyone inside chosen clusters. People in non-selected clusters have zero chance of being included, so equal probability across all individuals is not achieved.

So the method that guarantees equal chance for every member is simple random sampling.