5. The Basics of Statistical Inference

The overarching objective of statistical inference is to draw conclusions (make inferences) based on available sample data. In this chapter we generally assume that data have been acquired by observing the values of a random sample X ₁, X ₂, …, X _n ; recall from Sect. 4.​6 that a random sample consists of rvs that are independent and have the same underlying probability distribution (what we also called iid). For example, highway fuel efficiency of a certain type of vehicle might have a normal distribution with mean μ and standard deviation σ. Then each observed fuel efficiency value would come from this normal distribution, with the various observed values obtained independently of one another—a normal random sample. Or the number of blemishes on a new type of DVD might have a Poisson distribution with mean value μ. If n of these disks were to be randomly selected and the number of blemishes on each one counted, the result would be data from a Poisson random sample. In either example, the values of the parameters would typically not be known to an investigator. The sample data would then be used to draw some type of conclusion about these values.