1.2 - Samples & Populations

We often have questions concerning large populations. Gathering information from the entire population is not always possible due to barriers such as time, accessibility, or cost. Instead of gathering information from the whole population, we often gather information from a smaller subset of the population, known as a sample.

Values concerning a sample are referred to as sample statistics while values concerning a population are referred to as population parameters.

Population
The entire set of possible cases
Sample
A subset of the population from which data are collected
Statistic
A measure concerning a sample (e.g., sample mean)
Parameter
A measure concerning a population (e.g., population mean)

The process of using sample statistics to make conclusions about population parameters is known as inferential statistics. In other words, data from a sample are used to make an inference about a population.

Inference about a population

Inferential Statistics
Statistical procedures that use data from an observed sample to make a conclusion about a population

Example: Student Housing Section

A survey is carried out at Penn State Altoona to estimate the proportion of all undergraduate students living at home during the current term. Of the 3,838 undergraduate students enrolled at the campus, a random sample of 100 was surveyed.

  • Population: All 3,838 undergraduate students at Penn State Altoona
  • Sample: The 100 undergraduate students surveyed

We can use the data collected from the sample of 100 students to make inferences about the population of all 3,838 students.

Example: Polling Teachers Section

Science Teacher

Educational policy researchers randomly selected 400 teachers at random from the National Science Teachers Association database of members and asked them whether or not they believed that evolution should be taught in public schools. They received responses from 252 teachers.

  • Population: All National Science Teachers Association members
  • Sample: The 252 respondents

The researchers can use the data collected from the 252 teachers who responded to the survey to make inferences about the population of all National Science Teachers Association members.

Example: Flipping a Coin Section

A fair coin is flipped 500 times and the number of heads is recorded.

  • Population: All flips of this coin
  • Sample: The 500 flips recorded in this study

We can use data from these 500 flips to make inferences about the population of all flips of this coin.