I have a little doubt regarding the confidence intervals.
I know that if I enlarge the sample size, then the amplitude of the interval will be smaller, therefore, the interval will be more precise, but I also think that, as a result of this, the probability that the confidence interval will be correct will be lower since the area under the curve(confidence level) between a narrower interval will be smaller.
So, I can say this?:
If the sample size grows, the accuracy of the interval will increase, however the probability of success of the interval will decrease.
