Why is the t-distribution more variable and flatter than the normal distribution?
For z scores and t scores, both have x-bar - mu in the numerator but the
denominators are different. For z, the bottom does not vary provided
all samples are the same size and chosen from same population, basically
the standard error is the same for every sample. But with t
distribution the standard deviation and thus the standard error change
from sample to sample, causing more variability which makes flatter and
more spread out. With larger sample size this variability decreases.