Question

What happens to the width of a confidence interval if the sample size increases, but all other quantities involved (e.g., the coverage probability and population variance) remain fixed? Please provide both an intuitive and mathematical explanation of your answer

Answer 1

Intuitively:

When the sample size increases, you got more data points.

If data increases, then the you have a greater probability that your point estimate lies inside the same set of end intervals. Hence, the width of CI decreases.

Mathematically, its given by:

X+/- Z*Sigma / sqrt(n)

So, increase n, and the margin of error decreases( 2nd term here), or the width ( or ME) is decreasing.

Hence, the Width of the whole term decreases. ( CI decreases)