Question

An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand. Is this an example of a simple random sample? Yes, because each buyer in the sample had an equal chance of being chosen. Yes, because car buyers of every brand were equally represented in the sample. No, because every possible 400-buyer sample did not have an equal chance of being chosen. No, because the population consisted of purchasers of four different brands of car.

Answer 1

Answer: The correct option is C. No, because every possible 400-buyer sample did not have an equal chance of being chosen.

Explanation: A simple random sampling technique is when a subset of individuals is chosen from a larger set or population, in a manner that each individual is chosen at random and entirely by chance, and each individual has equal probability of being chosen.

Therefore, a simple random sample will require that every one of the sampled set of 400, has an equal chance of being selected.

In the scenario given above, there was a 100 percent probability that the sample would include 100 purchasers of each brand of car but there was a zero percent probability that the sample would include, say, 95 Ford buyers, 105 Honda buyers, 90 Toyota buyers, and 110 GM buyers.

Hence, all possible samples of size 400 did not have an equal chance of being selected; so this cannot be a simple random sample.

Because each car buyers was equally represented in the sample given above has no bearing on whether the sampling method was simple random sampling.