 # Sampling distribution of the mean

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This video explores the concept of a sampling distribution of the mean. It highlights how we can draw conclusions about a population mean based on a sample mean by understanding how sample means behave when we know the true values of the population.

### Prerequisite Knowledge

• Be able to identify and distinguish between a population and a sample, and between parameters and statistics
• Be familiar with methods of summarizing data sets, such as mean, standard deviation and histograms
• Be able to recognize probability models as distributions with shape, centre, and spread particularly the Normal distribution

### Learning Objectives

• Explain the concepts of sampling variability and sampling distribution
• Describe properties of the sampling distribution of the sample mean when the sample size is large
• Calculate the standard error of a sample mean
• Explain how the sample size influences the sampling distribution of the mean
• Distinguish between the sampling distribution of the mean and the distribution of a sample of n observations

### Description

This video explores the concept of a sampling distribution of the mean. It highlights how we can draw conclusions about a population mean based on a sample mean by understanding how sample means behave when we know the true values of the population.

### Suggested Uses, Tips and Discoveries

• Students can watch the video before class, giving them the flexibility to engage with the video in the way that suits them (pausing, rewinding). Students are primed for class and lecture time can be spent applying that knowledge in engaging and collaborative ways.
• Students can watch the video after they have learned the material in lecture. The video could be used as a refresher of the material before an exam or to review concepts they didn’t understand in class.

### Related Resources

#### Confidence interval for a population mean

This video discusses the concept of a confidence interval for a population mean. It emphasizes the interpretation of a confidence interval and explores the connections between the interval width, margin of error and sample size.

• Marin, Mike

2017

Everyone

### Original Video 1.mp4

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Please use this identifier to cite or link to this resource: `https://statspace.elearning.ubc.ca/handle/123456789/77`