Simple Random Sample vs. Random Sample Refer to the definition of simple random sample here and its accompanying definition of random sample enclosed within parentheses. Determine whether each of the following is a simple random sample and a random sample.


a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team.

Verified step by step guidance

1. Understand the definition of a simple random sample: A simple random sample (SRS) is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. An SRS is meant to be an unbiased representation of a group.
2. Understand the definition of a random sample: A random sample is a sample that is chosen randomly from the population, but it does not necessarily mean that each member of the population has an equal chance of being selected.
3. Analyze the given scenario: In this problem, there are 30 teams, each with 25 players. The names of the teams are printed on index cards, shuffled, and one card is drawn. The sample consists of the 25 players from the selected team.
4. Determine if the sample is a simple random sample: Since only one team is selected and all players from that team are included, not every player in the league has an equal chance of being selected. Therefore, this is not a simple random sample.
5. Determine if the sample is a random sample: The selection of the team is random, as it is based on shuffling and drawing a card. Therefore, this is a random sample, but not a simple random sample.

Key Concepts

Simple Random Sample

A simple random sample is a subset of a statistical population where each member of the subset has an equal probability of being chosen. This means that every possible sample of the same size has the same chance of being selected. It ensures that the sample is unbiased and representative of the entire population.

Random Sample

A random sample is a sample that is selected from a population in such a way that each member of the population has a known, non-zero chance of being included. Unlike a simple random sample, the probabilities may not be equal, but randomness is still a key feature to avoid bias in the selection process.

Sampling Method

The sampling method refers to the process used to select individuals from the population to be included in the sample. In the context of the question, the method involves shuffling index cards representing teams and drawing one, which affects whether the sample is simple random or just random, based on the equal probability criterion.