Random samples should act in a random (unpredictable) way... right? WRONG! As samples grow in size, the probability of randomly selecting samples with specific means becomes easier and easier to predict. I show how this is the logical result of the Central Limit Theorem using an easy to follow example.
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Here is an example of the most common exam style of question from Chapter 9. This question includes almost everything you’ll be expected to answer from this chapter in terms of sample means.
Chapters 8 and 9 both ask probability questions, they both work with continuous data, and they both rely on standard normal tables for finding probabilities - So how do we know when to use Chapter 9 techniques? It comes down to sample sizes and working with averages...
Some questions ask for the probability that the sample mean falls within a given range. The opposite is also asked: Which sample mean occurs with a given probability? To solve this, we just need to reverse the order of some of the steps in our solution.
Some questions can be solved by the techniques in more than one chapter. There is a significant overlap between Chapter 7 binomial and Chapter 9 sample proportions. Both teach you how to find the probabilities of multiple nominal (binomial) outcomes. I explain here how Ch.9 sampling distributions can (sometimes) be the easiest way to solve a binomial problem.
The math in this kind of problem looks horrible, but I'll show you how we can find the probability of a difference in sample means quickly using the same simple steps that have worked throughout the rest of the chapter.
Test your understanding of Chapter 9: Sampling Distributions - each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.