Valid Inference

A valid inference is a conclusion drawn from a sampling of a population that is highly likely to be true. This type of inference is based on representative samples and supported by sufficient data. Consider an example where a survey was conducted on the people of a city asking for their heights.

Here are more details of the survey and what it found. The survey was conducted in a simple random sample of $250$ inhabitants of a city. It found that the average height of the people in the sample is $5$ feet $7$ inches. This is enough information to make an inference about the average height of all inhabitants of the city. The average height of all inhabitants of the city is about $5'7.$ This inference is valid because of the following characteristics of the study.

1. A simple random sample is usually unbiased.
2. The number of participants 250 is a relevant sample size.

It should be noted that the sample size should be as big as possible. For small populations, a relevant sample size is about 10 % of the population. However, with big populations this can be hard or impossible to achieve, so, as long as the sample size is around 300, the sample can lead to valid inferences if it is unbiased.