5. Confidence Intervals

An introduction to confidence intervals.

I derive the appropriate formula for a confidence interval for the population mean mu, when sampling from a normally distributed population with a known value of sigma. (The purpose of this video is to show the rationale behind the confidence interval formula for mu.) I do not work through an example in this video; I … Read more

An introduction to confidence intervals for the population mean mu. These methods are appropriate when we are sampling from a normally distributed population, where the population standard deviation sigma is known. When the population standard deviation is not known, as is usually the case, we need to use a slightly different method (a method based … Read more

I show how to find the appropriate z value (using the standard normal table) when calculating a confidence interval.

Interpreting a confidence interval for the population mean mu. Some reasonable interpretations are discussed, as are some common misconceptions. Many of these concepts hold for confidence intervals for other parameters.

A look at the effect of various factors (the standard deviation, the sample size, and the confidence level) on the margin of error of a confidence interval for the population mean.

Intro to confidence intervals for mu based on the t distribution. These methods are appropriate when we are sampling from a normally distributed population and the population standard deviation (sigma) is not known.

A brief non-technical introduction to the t distribution, and how it relates to the standard normal distribution.

I find the sample size required to obtain a given margin of error in a confidence interval for mu. I discuss the appropriate formula and work through an example.

A discussion of the assumptions when using the t procedure to construct a confidence interval for the population mean mu. The assumptions are discussed, and the effect of different violations of the normality assumption is investigated through simulation.