Say you have an experiment involving 100 oranges tracking the probability that an orange is rotten. You test for a probability p and your null hypothesis is p < 0.01 (all oranges coming from a good farm) and your alternative hypothesis is p > 0.99 (all oranges coming from a bad farm).
For a Type 1 Error probability of 0.05, you basically just need more than 2.64 oranges to be rotten to reject the null hypothesis with a 5% chance to be wrong.
Now, since we rejected the null hypothesis, we automatically accept the alternative hypothesis of p > 0.99.
In my opinion, that also seems absurd.
So have I made any mathematical or logic error in the process above?