Consider a simple linear model: I have obtained a prediction interval of $(37, 66)$ and a point prediction of $52$. (the problem behind is not a concern I reckon, for the sake of the question).
Now I know that if the actual response will be $\geq 50$, then a plant will grow, whereas if it is less than $50$, it will fail to grow.
The question is to interpret the prediction interval (and the point prediction I guess), to understand whether there is evidence that the plant will not grow.
How do I go about interpreting this?
For example the upper end of the interval of prediction is bigger than $50$, and also the predicted value is slightly bigger than $50$, however the lower end of the prediction interval goes as far down as $37$.. so how does a statistician interpret this? Is there evidence? And if I need to use some mathematical tools, what techniques should I use to see if there is evidence?
This is the problem with intervals...you lose a lot of probabilistic information. You should look at the likelihood ratio of response $\geq 50$ vs $<50$. If you are using a Bayesian model, then the posterior odds ratio or predictive probability of $\geq 50$ may be useful.