Is the method of testing two wrestlers from each high school team a simple random sample?

Is the method of testing two wrestlers from each high school team a simple random sample?

• A. Yes, because all wrestlers are equally likely to be chosen
• B. No, because not all possible groups of 32 wrestlers could have been the sample
• C. Yes, because it uses random selection
• D. No, because teams are treated as blocks

Answer: (B)

The method of testing two wrestlers from each high school team does not qualify as a simple random sample primarily because simple random sampling means that every possible group of individuals from the population has an equal chance of being chosen. In this case, by selecting two wrestlers from each of the teams, the sample is inherently limited to those teams and cannot create a sample comprised of all possible wrestlers across the entire population of teams. This constrains the sample space and implies that some combinations of wrestlers cannot be selected because they are not represented among the teams, meaning that groups of wrestlers that include individuals from different teams or that have a different number of wrestlers could not be formed. Moreover, while it’s true that random selection might be involved in picking the wrestlers from their respective teams, it does not fulfill the criteria needed for a simple random sample since not all potential samples across the total population of wrestlers are equally possible or likely to occur. This aspect emphasizes that the sampling method does not provide a comprehensive representation of the population, which undermines its status as a simple random sample.

The method of testing two wrestlers from each high school team does not qualify as a simple random sample primarily because simple random sampling means that every possible group of individuals from the population has an equal chance of being chosen. In this case, by selecting two wrestlers from each of the teams, the sample is inherently limited to those teams and cannot create a sample comprised of all possible wrestlers across the entire population of teams. This constrains the sample space and implies that some combinations of wrestlers cannot be selected because they are not represented among the teams, meaning that groups of wrestlers that include individuals from different teams or that have a different number of wrestlers could not be formed.

Moreover, while it’s true that random selection might be involved in picking the wrestlers from their respective teams, it does not fulfill the criteria needed for a simple random sample since not all potential samples across the total population of wrestlers are equally possible or likely to occur. This aspect emphasizes that the sampling method does not provide a comprehensive representation of the population, which undermines its status as a simple random sample.