In this situation, the Chief Engineer wants to be able to report on the fuel economy for all of the upgraded vehicles for the entire company. Vehicles are being upgraded at several facilities, and consumers will be able to purchase them from all over the country. In a perfect world, the engineer would measure the fuel economy of every single vehicle receiving the upgrade. This way, there would be no question as to the new, upgraded fuel economy.

However, as is with nearly every case like this, the engineer is limited by how many vehicles can be tested. A sample of 25 cars is a fine number; the bigger the better, but this is certainly enough to gain some insight in the situation. The issue is that the engineer is being told to only sample vehicles from the most advanced facility. This will result in skewed data. When we take a sample, every subject in the population should have an equal chance of being selected. In this case, every vehicle across the entire company that is getting the upgrade should have an equal chance of being part of the sample. If the engineer is limited to only selecting vehicles from one facility, then the results would only apply to that facility. They would not be able to generalize the results to all vehicles.

The best setup would be to list all of the vehicles from all of the facilities that will be receiving the upgrade. Then, have some random process choose 25 cars from that list, no matter what facility it is from, and use that list to take measurements. This way, every upgraded car across the whole company had a chance of being measured; this will allow for the results to be generalized across the entire company (not just one facility).