Reliability Factors based on T distribution

CFA Level I
#1

Question:

Find the reliability factors based on the t-distribution for the following confidence intervals for the population mean:

A 99 percent confidence interval, df=20

So, apparently at the 99 percent confidence interval we use the reliability factor t(.005) and for df 20 this translates to a factor of 2.845 where looking at the t chart.

This confuses me. When i see 99 percent confidence interval i think [mean(plus/minus)2.58s].

Can someone please clarify this for me?

Thanks!

#2

You’re thinking of a z-distribution or a t-distribution based on a large degrees of freedom. The key here is that the t-distribution is based on the degrees of freedom, which you say is 20. The distribution here has a different shape than the z-distribution, and the critical value is different (larger).