Final answer:
To create a simple random sample (SRS), each athlete must have the same chance of being selected. Stratified, simple random, and cluster sampling are different methods, with simple random sampling being the appropriate choice for an SRS.
Step-by-step explanation:
To be considered a simple random sample (SRS), the athletes in the sample of size n must have the same chance of being selected from the population as any other athlete. In other words, every individual in the population must have an equal opportunity to be included in the sample. This process ensures that the sample reflects the population well and avoids bias.
Looking at the different types of sampling methods provided in the SEO material, the correct choice for creating an SRS would be to use a method where each athlete has a known and equal chance of being selected. Applying this to the provided scenarios:
- Stratified sampling is used when the researcher divides the population into subgroups (strata) and samples from each subgroup. An example of this is when a sample of 100 high school students is taken by organizing the students' names by grade and then selecting a number of students from each.
- Simple random sampling is when each member of the population has an equal chance of being selected, similar to drawing names out of a hat.
- Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters to be included in the study.
To generate a simple random sample of the 100 athletes, the researcher could assign each athlete a unique number and use a random number generator to select the athletes for the study, ensuring that each one has an equal chance of being chosen.