As we saw in the last section, we use a hypothesis test when a claim has been made and we want to test it as a statistical hypothesis. Now that we are more aware of the sort of situation that will lead us to conduct such a test, let's have a look at how the test works. What we will do over the next two sections of this chapter is see how the philosophy of hypothesis testing leads us to conduct the test in the way that we do. We will cover the general methods and tools used in the field. In the later sections of this chapter, we'll move on to see specific examples of hypothesis testing for various population parameters.
As with estimation, the heart of the technique is in sampling distributions. If we are testing a claim about the population mean μ of a numerical variable X, then the sampling distribution of the mean, X, will play a large role. If we are testing a claim about the population proportion π for a category of a categorical variable Y, then the sampling distribution of the proportion, P, will apply.
In fact, our whole way of acquainting ourselves with the technique of testing will be very similar to how we did this with estimation. That is, we will focus on sampling distributions like X or P, which give a fairly precise description of what is going on in a test.
As we will see in the next section of this chapter, and just as we did with confidence interval estimation, the complete methodology involved in a formal hypothesis test will involve relating such sampling distributions as X and P to the standard normal distribution. But we won't travel that far in this section. In this section, we will focus on the important conceptual components of conducting a hypothesis test, which are: