Sampling Framework

Let’s introduce some terminology and notation as well as statistical definitions related to sampling. Keep in mind, however, that all of the concepts underlying the terminology, notation, and definitions tie directly to the concepts underlying our tactile and virtual sampling activities. It’ll simply take time and practice to become proficient in these concepts.

Terminology and notation

Let’s explore the terminologies and mathematical notations relating to sampling:

• Population: This is a collection of individuals or observations we’re interested in. This is also commonly denoted as a study population. We mathematically denote the population’s size using upper-case$N$. In our sampling activities, the (study) population is the collection of $𝑁$ = 2,400 identically sized red and white balls contained in the bowl.

• Population parameter: This is a numerical summary quantity about the population that’s unknown but we wish we knew. For example, when this quantity is the mean, the population parameter of interest is the population mean. This is mathematically denoted by the Greek letter $\mu$, pronounced as “mu.” In our earlier sampling from the bowl activity, however, because we’re interested in the proportion of the bowl’s balls that were red, the population parameter is the population proportion. This is mathematically denoted by the letter $𝑝$.

• Census: This is an exhaustive enumeration or counting of all $N$ individuals or observations in the population in order to compute the population parameter’s value exactly. In our sampling activity, this will correspond to counting the number of balls out of ...