Say I plan an experiment to test the null hypothesis of $H_0:\mu_1-\mu_2 = 0$ and, with a power analysis for a Student's $t$-test for independent samples, I find that samples of $n=10$ (per group) will give me power of 99.5% with the alternative hypothesis of $H_a: \mu_1-\mu_2=3$ with $\alpha=0.005$.
(Assume the statistical model is a good enough match to reality for the purposes of the analysis.)
Now I run the planned experiment and reject the null hypothesis. What is my inference regarding $H_a$?
It seems to me that any time I reject $H_0$ I implicitly accept the negation of $H_0$, but should I accept the planned point value of $H_a$?
A test where I accept the planning alternative whenever I reject the null would allow me to accept an alternative when the evidence do not actually favour it.
(Yes, there are several other questions an answers that are similar, but I have not found any that is explicit on this point, and I think clarity here will be useful.)