Populations and Samples Examples

Scientists measured the weight of 100 randomly selected buffalo, because there was nothing good on TV that evening. Their average weight was 1200 pounds. The buffalo, not the scientists. Identify the population, the sample, the parameter, and the estimate of this study.

The population is every individual that could possibly be of interest. We're talking buffalo here, so the population is all the buffalo. Yep, every single one.

Samples are a subset of the population. They should be randomly selected from the full population, so that the sample will be representative of the whole population. The 100 buffalo measured are the sample here.

Parameters are some aspect of the population that are unknown, but that we want to estimate. The average weight of the buffalo population is a parameter, which means the estimate is the average weight of the sample.

A researcher wants to know if people prefer to butter their toast on the top or on the bottom. She buys ad space on several popular websites asking people to take her survey. She gets over 1000 responses, and concludes that people prefer to butter the bottom of their toast. What is the problem with how this study was carried out?

Having random people ask to participate in a survey is different from randomly selecting them. Everyone who responded to the ad volunteered to do so. Maybe they were bored, or the subject (somehow) interested them. Either way, the group of people who volunteer for a study can be different from the group of people who don't volunteer, which results in a volunteer bias.

Just how destructive is the Kool-Aid Man? We went out and measured the size of the holes he had made in 20 walls. What kind of study is this: a sample survey, an experiment, or an observational study?

The easiest way to tell these types of studies apart is to figure out what role randomization is playing.

In a sample survey, we randomly select individuals from the full population to create a random sample. There's no mention of the walls we studied being randomly selected from a larger population. We probably just included every wall Kool-Aid had busted through. OH NO.

Experiments use randomization to put individuals into the control and treatment groups. We don't have two separate groups, so OH NO, this isn't an experiment.

Observational studies don't have randomization at all. They collect the data however they find it, which is just what we've done here. OH YEAH.