I have a some data that contains 100 elements. I can model it as a normal distribution using the t-distributionI have used the t-distribution to construct a confidence interval for unknown value of mu.
However, the five smallest values appear to be outliers and I tried to recalculate the confidence interval without these five values. This results in a larger confidence than before.
I expected that due to now using a smaller sample size, this would increase in a smaller confidence interval. I was hoping somebody could explain what factor has resulted in the smaller confidence interval.
In general, one would expect that a smaller sample would result in a larger (say $95\%$) confidence interval.
However, in the situation you describe, one could easily end up with a smaller (that is, better) confidence interval. That is because you were using the $t$ distribution. Discarding the outliers may have decreased the sample variance enough to account for the shrinkage in the confidence interval.