1. Samples & Populations

Four Fundamental Concepts

• Inferential Statistics

  • Aim is to make generalizations about populations based on sample data.

  • Essential for understanding samples and population dynamics.

The Situation

• Given task to estimate the average age of full-time students at Dawson College.

  • Sample: 50 students

  • Population: 10,000 students

  • Importance of exploring sample concepts outlined.

#1: Random Sampling

• Definition and Criteria:

  1. Every unit in the population has an equal chance of selection.

  2. Selection of one unit does not influence the selection of another.

  3. All combinations must be possible, recognizing that extreme combinations occur but are rare.

• Random sampling requires meeting selection criteria, despite perceived randomness.

Population vs. Random Sample

• First step: Identify a representative sampling frame.

• Example: Obtain a complete list of all Dawson College students from the Registrar to establish the sampling frame.

#2: Sampling Error

• Concept of sampling error acknowledges numerous potential samples from the same population.

• No sample holds special status; accuracy varies per sample.

• Sampling error: Difference between sample statistic and population parameter caused by chance.

Emphasis on Sampling Error

• Acknowledges that any sample represents one of an infinite number of possibilities.

• Recognition of sampling error is critical for valid inferential statistics.

#3: The Sampling Distribution of Sample Means

• Concept: Repeated sampling of the same size yields different means, which can be plotted as a histogram.

• Result: Distribution of sample means emerges from varying samples.

• Key Characteristics:

  1. Each distribution has a mean.

  2. Standard deviation (called standard error of the mean here).

Key Terms Review

• Statistic: Descriptive measure of a sample.

• Parameter: Descriptive measure of a population.

• Notation:

  • Sample Mean: x

  • Population Mean: μ (mu)