Statistical Inference: A Short Course

10.9 Reporting The Results of Statistical Hypothesis Tests

How are the results of hypothesis tests typically presented? As we shall now see, so-called p-values are used. If we harken back to our classical hypothesis test procedure, one of the steps was to select a level of significance or α value. Hence α is our “chosen” level of significance. An alternative to this action is to let the data itself determine the “actual” level of significance of the test, that is, we shall determine the test's p-value—its observed or actual level of significance. Specifically, the p-value is the probability of obtaining a calculated value of the test statistic at least as large as the one observed if H₀ is true. In this regard, the larger the p-value, the more likely it is that the null hypothesis is true; and the smaller the p-value, the more likely it is that the null hypothesis is not true.

Thus a test of significance is based on the notion that: a sample outcome that would happen only infrequently if H₀ were true provides compelling evidence that H₀ is not true. And we assess the strength of the evidence by determining a probability (a p-value) that reflects how infrequently this outcome would occur if H₀ were true.

For instance, suppose we are testing H₀: μ = μ_o versus H₁: μ > μ_o and we get a calculated value of = 1.79. What is the test's p-value? To answer this, we need to execute the following ...