Assignment

This week we are focusing for the first time on the concept of hypothesis testing. Unfortunately, some people make this concept much more complicated than it needs to be. The phrases "no effect" or "no change" are sometimes used to describe the null hypothesis (even Triola uses this description), but that phrase is not always accurate. The statement that the null hypothesis always has something to do with zero is not always correct either. The statement that the null hypothesis is the opposite of what you wish to verify is not always correct either. All of these generalizations are often true, because of the way different disciplines use the process of hypothesis testing, but thinking that they are the definition of the null hypothesis has the effect of hiding what the null hypothesis really does. In your answer to this question do not use any of the ideas that I have discussed above. If you do, I will mark your post with a U, because you have not responded to the question that I am asking here. By avoiding these generalizations, we can get to the real meaning of the null hypothesis. It is often (maybe even usually) for the purposes as described here, but that does not define what the null hypothesis actually is. What a concept is and how it is used are not the same thing.

1. Explain what the null hypothesis is in mathematical terms and how it is related to the question that is being investigated (also know as the research hypothesis). Your description of the null hypothesis should reflect the fact that the null hypothesis is a mathematical statement, not some philosophical construct. If you start discussing something like "the null hypothesis is something that you think is true (or false, whichever), you are going in the wrong direction. Be sure and explain how the null hypothesis is determined from the research hypothesis as part of your answer. You should be able to answer this question directly from material you find in the text and in my videos and power points. Chances are very good that information you find from other sources will leave you confused and probably heading in the wrong direction

2. One of the areas which seems to really confuse students every time I teach this course is understanding the difference between a proportion and a mean. They are parameters (for populations) or statistics (for samples) that are designed for different kinds of data, but I frequently see students making use of methods (and terminology) for one when they should be using the other. In this question, I want to try to help avoid those problems.

1. What is a proportion and what kind of data is it designed for (remember the distinction between categorical and quantitative data)?

2. How is the proportion different from the mean? What kind of data is the mean designed for (again remember the distinction beween categorical and quantitative data)?

3. What are the similarities and differences in dealing with hypothesis testing for each?

4. In reading project proposals in Week 5, I almost always end up with students who get proportions and means confused. Why do you think this happens?

3. Most statisticians prefer to describe the results when the P-value is greater than level of significance (or when the test statitics is not in the critcal region) by saying "the null hypothesis is not rejected." Why do you think that this language is preferred over saying "the null hypothesis is accepted"?