Simple Random Sample vs. Random Sample Refer to the definition...

Question

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.

Accepted Answer

Hello, everyone. Let's take a look at this question together. In a national basketball League, there are 20 teams, each with an active roster of 15 players. The names of the teams are written on 20 index cards, shuffled, and 1 card is drawn. The sample consists of the 15 players on the active roster of the selected team. Is this an example of simple random sample or a random sample? So which of the following answer choices is the correct answer? Is it answer choice A, a simple random sample, answer choice B, a random sample, answer choice C, both of these, or answer choice D, none of these? Well, in order to solve this question, we have to recall what we have learned about a simple random sample and a random sample, which we know that a simple random sample is where every individual in the population has an equal chance of being selected. And a random sample is where a sample is chosen using some random method, but it may not be a simple random sample. And in order to determine if this is an example of a simple random sample or a random sample, we have to look at the selection method, which selection involves randomly drawing a card, of which the Cards have the team name written on them, and this method ensures that each team has an equal chance of being selected. And since each team has an equal chance of being selected, we know that this selection is a random sample. And we also know that it is not a simple random sample as a simple random sample in involves every individual in the population having an equal chance of being selected. However, the entire team is being selected and not the players individually, so it cannot be a simple random sample making answer choice be the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Simple Random Sample

Random Sample

Sampling Method

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