Text Font Conventions

Key concepts - You will be responsible for knowing a number of definitions of key concepts. You may be asked to give an accurate definition and example of any of the key concepts. Key concepts are in italics, bolded and colored red throughout the notes.

Critical points - There are some points that require extra emphasis because they are fundamental to the example or concept being discussed. Critical points are bolded, in italics and colored orange.

Course learning objective questions - These are the questions given in the learning objectives document.

Lecture 7

This week, we use what we know about sampling distributions to make decision about the features of the population we have sampled from. Essentially, the idea is this...We don't know what the features of the population are that we have sampled from, all we have is the sample. But we would like to at least say something about the population we have sampled from. One thing we can do is assume that the population we have sampled from has a certain feature (say a mean of 100) and then use sample information and the theory of sampling distributions to make a decision about whether or not our assumption is true. That is the essence of the method of hypothesis testing. So, this week, we look at the procedure of hypothesis testing. Let's first get straight the technical details of the procedure.

1) Hypothesis testing technical video....here

In the next video, let's just look at some of the logical features of hypothesis testing. In this video, we use the example of the OJ Simpson trial to demonstrate the logic of the hypothesis testing decision procedure.

2) The logic of hypothesis testing....here

It's difficult to understand hypothesis testing without knowing something about how we use it to make decisions about the features of populations. In the following video, we look at the use of hypothesis testing to make a decision about the mean of a population from which a set of observations has been sampled.

3) An example of the use of hypothesis testing....here

In the previous video, I made reference to four very important concepts...the critical value, the observed result, the p-value and alpha. Let's take a look at the technical videos for these concepts.

4) The critical value and observed result....here

5) Alpha....here

6) The p-value....here

In the previous video, I made reference to the concepts of power and beta. These are two probabilities that are relevant when the null hypothesis is not true. There are an infinite number of things that could be true when the null is not true (so, for instance, if the null is that the mean of the population is 100, what could be true if that is false is that the mean is 100.0000001 or 100.0000002 or 100.0000003 and so on). We call the set of distributions that might exist if the null is not true, alternative distributions. Power and Beta are probabilities we find in alternative distributions. So, let's take a look at the technical videos for beta and power.

7) Beta technical video....here

8) Power technical video....here

Now let's take a look at some examples of questions you might be asked on the test about beta, power, the p-value etc.

9) Hypothesis testing test question examples....here

By the time you have watched and taken notes on the videos above and worked to understand them and commit to memory the names, definitions and symbols associated with each concept, you should understand what hypothesis testing is, and all of the concepts relevant to hypothesis testing. So, for instance, alpha, beta, power, p-value, observed result, critical value rejection region, null distribution, alternative distribution, etc. You should also be able to begin to answer learning objectives questions 17-21. Now, these are tricky questions so you should ask me about them on the discussion board. But, for now, take a complete look at my answer to question 17. This video goes through my example of the logic of hypothesis testing...the first date example...and demonstrates all the relevant concepts in the example. That is, the concepts of null distribution, alternative distribution, alpha, beta, power, the p-value, observed result and critical value. You should develop your own example and you may well need me to help you in doing that. So ask away on the discussion board. Note: If I say "As I said in class" I mean...as I have said in previous videos.

10) First date example....here

Finally this week, here is some help for learning objectives questions 17, 18 and 19.

11) Learning objectives questions 17, 18 and 19 help....here.

That's it for this week. Feel free to ask questions on the "Course Questions" discussion board in Blackboard. I will answer questions on Tuesday thru Thursdays of each week.

Now on to lecture 8.