Question at position 26 Each of the 30 NBA teams has 14 players. A sample of 60 players is to be chosen as follows. Each team will be asked to place 14 cards with its players' names into a hat and randomly select two names. The two names from each team will be combined to make up the sample. Will this method result in a simple random sample of 60 NBA players?Yes, because each player has the same chance of being chosenNo, because this is a cluster sampleNo, because this is a blocked sampleYes, because each team is equally representedNo, because this is a stratified sample

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BlackTom AI · Accepted Answer

Question restatement: A sample of 60 NBA players is chosen by asking each of the 30 teams to place 14 cards (one for each player) into a hat and randomly draw two names from that team. The two names from each team are then combined to make the 60-player sample. The question asks whether this method yields a simple random sample of 60 players.

Option A: Yes, because each player has the same chance of being chosen. This is not correct. Although, within each team, every player has the same chance of being drawn (2 out of 14, i.e., 1/7), the overall method does not give every possible 60-player subset an equal probability. The constraint of selecting exactly 2 players from each team biases the joint distribution of samples and excludes many 60-player combinations (e.g., samples with more than 2 players from a single team or with uneven team representation). Hence it is not a simple random sample.

Option B: No, because this is a cluster sample. This is inaccurate. A cluster sample would involve sampling entire groups (clusters) and using all members of the chosen clusters. Here, we do not sample entire teams; we only pick 2 players from each team, so it’s not a cluster design.

Option C: No, because this is a blocked sample. While there is a blocking factor (team), the operation is more accurately described as stratified sampling, where each stratum (team) contributes a fixed number of elements. Calling it a blocked sample can be misleading; the intended characterization is stratified sampling rather than a classical blocked design for experiments.

Option D: Yes, because each team is equally represented. Although this describes equal representation by team, it does not guarantee that the overall sample is a simple random sample. Equal representation across teams is a feature of this design, but simple random sampling requires every possible set of 60 players to be equally likely, which is not satisfied here.

Option E: No, because this is a stratified sample. This is the correct reasoning. The population is divided into strata (teams), and from each stratum exactly 2 players are chosen (i.e., a fixed number per team). This is the hallmark of stratified sampling, which does not produce a simple random sample of the entire 60-player set because the selection probabilities are constrained within each team rather than treating all 420 players identically as in simple random sampling.

Summary view: Each option is examined for whether it yields a simple random sample. The method corresponds to a stratified sampling design (fixed 2-per-team) and thus is not a simple random sample; therefore, the correct classification is that it is not simple random because it is stratified.

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