Statistical inference is an activity!
The best way to master hypothesis tests is to do them, not just to read about them. The first three sections of this chapter developed the method that you will follow when you conduct a hypothesis test. The step-by-step guide at the end of the third section will prove to be a helpful resource if you have to do such a test. And the fourth section of this chapter gave us some insight into what things a statistician will have to consider when they are about to embark on a hypothesis test. But in order to get used to these methods and these considerations, you will have to actually do some tests!
So conducting tests is what we will be doing in this section. We will cover a few hypothesis tests in detail to become familiar with the sorts of things that you have to think about when you do such a test, but also just to get practice. We will also see some situations where there are a few extra considerations to ponder.
One of these in particular will have a fairly wide impact on the methodology of the test. If you are testing a population mean, μ, and you don't know the population standard deviation, σ, then you will have to use t-distributions instead of the standard normal distribution. Don't worry: the basic method is the same, and we will cover it in this section.
We will also see an example in which the test statistic is quite 'close' to a critical value. Remember that the decision in a hypothesis test rests on whether or not the test statistic is in the region of rejection. But what if it is 'near the edge', so to speak? We will see an example in this section in which this occurs and we will discuss what to do - or at least what to think about!
Across the examples in this section, we will cover every aspect of a hypothesis test for the mean or the proportion. Together with the earlier sections of this chapter, you will see the full spectrum of possible hypothesis tests you might come across. For example, earlier in this chapter we studied an example of a two-sided test for the population proportion π. So in this section, we will focus on a one-sided test. Similarly, for the population mean μ in this section we will focus on a two-sided test since we looked at a one-sided test earlier. The larger the variety of situations that you see, the better you will get at conducting a test!