0

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.

enter image description here

enter image description here

ESCM
  • 3,161
  • As far as the commonly adopted practice goes, increasing the sample size does NOT lower the confidence level. The confidence level $\alpha$ is fixed by construction. – Lee David Chung Lin Jul 29 '19 at 21:22
  • @LeeDavidChungLin I know this property: If the amplitude of the interval decreases, the level of confidence decreases. According to that, i can say that if the sample size increases, the amplitude decreases, therefore the confidence level decrease. So why do you say it doesn't affect? – ESCM Jul 29 '19 at 23:32
  • Usually the interval is constructed for a fixed $\alpha$. If in your application the interval is constructed with something else fixed, then that's a different story. – Lee David Chung Lin Jul 30 '19 at 00:35

0 Answers0