The following is an example of a hypothesis testing from an introductory stats book.
A medical research team has been given the task of evaluating a new laser treatment for certain types of tumors. Consider the following two scenarios:
Scenario 1: The current standard treatment is considered reasonable and safe by the medical community, is not costly, has no major side effects, and has a known success rate of 0.85 (or 85%).
Scenario 2: The current standard treatment sometimes has serious side effects, is costly, and has a known success rate of 0.30 (or 30%).
The solution provided by the books is as follows:
In the first scenario, the research question of interest would probably be “Does the new treatment have a higher success rate than the standard treatment?” Unless there is convincing evidence that the new treatment has a higher success rate, it is unlikely that current medical practice would change. With p representing the true proportion of success for the laser treatment, the following hypotheses would be tested:
H0: p=0.85 versus Ha: p > 0.85
In this case, rejecting the null hypothesis would require convincing evidence that the success rate is higher for the new treatment.
In the second scenario, the current standard treatment does not have much to recommend it. The new laser treatment may be considered preferable because of cost or because it has fewer or less serious side effects, as long as the success rate for the new procedure is no worse than that of the standard treatment. Here, researchers might decide to test
H0: p=0.30 versus Ha: p<0.30
My question is why in the 2nd scenario alternative hypothesis is