Answer:
The questions are about the sampling strategies used to test baseball players for performance-enhancing drugs. The sampling strategies are methods of selecting a subset of individuals from a population to collect data from. There are different types of sampling strategies, such as simple random sampling, stratified random sampling, cluster sampling, systematic sampling, and convenience sampling. Each type has its own advantages and disadvantages, depending on the research objectives and the characteristics of the population.
Here are the answers to the questions:
Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. This is an example of cluster sampling. Cluster sampling is a type of probability sampling where the population is divided into groups, called clusters, and a random sample of clusters is selected. Then, all the members of the selected clusters are included in the sample. This method is convenient and cost-effective when the population is large and geographically dispersed, and the clusters are representative of the population. However, it may introduce more sampling errors and variability than other methods, especially if the clusters are heterogeneous.
Officials number all of the players in the league, select 40 unique random integers, and then drug test those players whose corresponding numbers were drawn. This is an example of simple random sampling. Simple random sampling is a type of probability sampling where each member of the population has an equal chance of being selected for the sample. This method is easy to implement and ensures that the sample is unbiased and representative of the population. However, it may be difficult or impractical to obtain a complete list of the population, and it may not capture the diversity or complexity of the population if the sample size is too small and has characteristics.
Officials select two players at random from each team, and a drug-testing crew shows up unannounced to test the 2 players. This is an example of stratified random sampling. Stratified random sampling is a type of probability sampling where the population is divided into groups, called strata, based on some relevant characteristics. Then, a random sample of members is selected from each stratum. This method ensures that each stratum is proportionally represented in the sample, and it can reduce the sampling error and variability by accounting for the differences among the strata. However, it may require more time and resources to identify and sample the strata, and it may not be appropriate if the strata are not mutually exclusive or exhaustive.
Officials take an alphabetical list of all major league baseball players and pick a name at random from the list. Then they select every 20th player on the list to be drug tested. This is an example of systematic sampling. Systematic sampling is a type of probability sampling where the population is ordered in some way, and a fixed interval is used to select the sample. For example, the first element is selected randomly, and then every kth element is selected, where k is the sampling interval. This method is simple and efficient to implement, and it can produce a representative sample if the population is homogeneous and the order is random. However, it may introduce bias and error if the population is heterogeneous or the order is related to the variable of interest.