Statistical Inference: A Short Course

10.5 The Classical Approach to Hypothesis Testing

Armed with the concepts, we can now specify what is called the classical approach to hypothesis testing:

Set the level of significance α, the probability of incorrectly rejecting H₀ when it is actually true, equal to some small value (0.01 or 0.05 or 0.10). So if we set, say, α = 0.05, then if we take many random samples of size n from the population and we repeat our test procedure for each of them, then, in the long run, we are willing to make a TIE 5% of the time. Thus 5% is the proportion of time that our test methodology renders the incorrect result of rejecting H₀ when it is actually true. Then, in accordance with H₁, choose the critical region or region of rejection R so that the probability of obtaining a value of in R equals α when H₀ is rejected at the α level of significance.

The classical approach to hypothesis testing is executed by the following stepwise procedure for hypothesis testing:

1. Formulate H₀ (assumed true) and H₁ (locates R).

2. Specify α (determines the size of R).

3. Select a test statistic ( or t or U) whose sampling distribution is known (it is N(0,1) or t distributed) under the assumption that H₀: θ ...