# CHAPTER 5STATISTICAL TESTING

## 5.1 HYPOTHESIS TESTING

In Example 4.4, we were not concerned about the actual bounds of the constructed interval, but rather, whether the constructed interval contained the expected ratio of the variances. This is often the case in statistics. That is, the actual values of the interval are not as important as is answering the question: Is the sample statistic consistent with what is expected from the population? The procedures used to test the validity of a statistic are known as *hypothesis testing*. The basic elements of a hypothesis test are as follows:

- The
*null hypothesis*, H_{0}, is a statement that compares a population statistic, which is usually derived from project specifications or specifications for an instruments, with the population of a sample. This implies that the sample statistic is what is “expected” from the population. In Example 4.4, this would be that the ratio of the variances is statistically 1. - The
*alternative hypothesis*, H_{a}, is what is accepted when a decision is made to reject the null hypothesis, and thus represents an alternative population of data from which the sample statistic was derived. In Example 4.4 the alternative hypothesis would be that the ratio of the variances is not equal to 1, and thus the variance did not come from the same population of data. - The
*test statistic*is computed from the sample data and is the ...

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