Chapter 10
Testing Statistical Hypotheses
The predominant operational theme addressed in this book is that of statistical inference–drawing conclusions about a population via random sampling coupled with the use of probability theory to assess the reliability of those conclusions. There are two sides to the “inferential coin,” so to speak. These are estimation and testing. As indicated in Chapters 8 and 9, a confidence interval is used to estimate an unknown parameter using sample data. As we shall now see, a hypothesis test (or significance test) is carried out to determine how strong the sample evidence is regarding some claim or assertion about a parameter.
We previously found that confidence interval estimation was based upon the application of the sampling distribution of a statistic and its attendant probability reckoning. The same is true of hypothesis testing. That is, hypothesis testing also utilizes the concept of probability, obtained from the sampling distribution of a statistic, to determine what would happen if we applied our test procedure many times in succession in the long run. It is the notion of probability that enables us to specify, in a quantitative fashion, how credible our test results are.
