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. T

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

Solution Steps

This question is about understanding the concept of a simple random sample (SRS) in statistics. A simple random sample is one in which every member of the population has an equal chance of being selected, and every possible sample of the desired size has the same chance of being chosen.

In this scenario, the analyst selects 100 buyers from each of the four brands, making sure that each brand is equally represented in the sample. However, this method does not give every possible group of 400 buyers from the 10,000 total buyers an equal chance of being selected because it restricts the selection to exactly 100 from each brand, rather than allowing any 400 buyers to be chosen completely at random.

Therefore, the correct answer is: No, because every possible 400-buyer sample did not have an equal chance of being chosen.

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.

The analyst selects a sample of 400 car buyers by randomly sampling 100 buyers of each brand. This method ensures that each brand is equally represented in the sample. However, it does not give every possible group of 400 buyers from the 10,000 an equal chance of being chosen because it restricts the sample to exactly 100 buyers from each brand.

Given the definition of a simple random sample, the method used by the analyst does not allow every possible 400-buyer sample from the 10,000 to have an equal chance of being chosen. The sampling method is stratified by brand, ensuring equal representation from each brand, but it does not meet the criteria for a simple random sample because it does not allow for every possible combination of 400 buyers to be equally likely.