Width of confidence interval

[tiger]

How does the confidence interval change as the sample size changes.

[Adrian]

As n increases, the confidence interval shrinks.

By the central limit theorem, the sampling distribution of the mean approaches the normal distribution as n increases. Z(0.975)=1.96 is the smaller than the corresponding t-values t(df, 0.975). In addition, the standard error of the mean decreases as n increases, thus the width of the CI decreases (the CI shrinks) as n increases.