Here is how the process of statistical hypothesis testing works:
So the null hypothesis in this example is
Finally, because of the significant costs associated with defense testing, questions about how much testing to do would be better addressed by statistical decision theory than by strict hypothesis testing. Cost considerations are especially important for complex single-shot systems (e.g., missiles) with high unit costs and highly reliable electronic equipment that might require testing over long periods of time (Meth and Read, ). Voting a system up or down against some standard of performance at a given decision point does not consider the potential for further improvements to the system. A better objective is to purchase the maximum possible military value/utility given the constraints of national security requirements and the budget. This broader perspective fits naturally into a decision analysis framework. Concerns about efficient use of testing resources have also stimulated work on reliability growth modeling (see the preceding section).
The example states a 5% level of significance so (lpha = 0.5).
If the biologist set her significance level α at 0.05 and used the critical value approach to conduct her hypothesis test, she would reject the null hypothesis if her test statistic t* were less than -1.6939 (determined using statistical software or a t-table):
Testing of hypothesis problems .
The power question is fairly straightforward. Clearly there is now no single power for our test of the hypothesis, but a different power for each possible value of the binomial probability included in the alternative hypothesis. The power is a function rather than a single value. This function is described in detail in the next section for Example 4.2.