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.
Now that we have the probability distribution, finding the probabilities of specific outcomes couldn't be any easier. If you can add, you can do this!
Why work with samples when what we really want is the population data?
Just two simple keywords in this question identify it as a chapter 9 problem. I'll show you how to look for these kinds of questions on your test, and how to solve them
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.
Here I solve a full Chapter 7 exam question. First , I look at the language used in the question to identify which chapter's techniques are appropriate. Once this is determined to be a discrete probability distribution problem, I use a probability tree (learned in Chapt.6) to find all possible outcomes as well as their probabilities... to construct the Discrete Probability Distribution.
A comparison of the three methods of data collection covered in this chapter:
- Observational Data
- Experimental Data
- Survey Data
Most exams include this reverse chapter 8 question where you're giving a probability and asked for the boundary. Make sure you understand how to justify your answer for this type of problem.
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...
The variance of a probability distribution also differs (in its calculation) from what you learned in Chapter 4. I extend the tabular approach that I used to find the expected value (previous video) so be able to find the variance of x. The standard deviation of x is simply the square root of the variance (just like in Chapter 4)