JB 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.
A first look at hypothesis testing.
An introduction to Z tests for a population mean mu. These tests are appropriate when sampling from a normally distributed population where sigma is known. I discuss the hypotheses and the underlying logic, and work through an example. I do not discuss the rejection region or p-value in an in-depth way in this video – … Read more
I work through a few quick examples of determining what area corresponds to the p-value in one-sample Z tests on the population mean mu. The same logic holds for other types of test. I assume that you know how to find areas under the standard normal curve.
An introduction to the concept of the p-value in a Z test. This video discusses the p-value in the context of a Z test for one mean, but the same logic holds for other Z tests.