The degree of normality in the data.
The degrees of freedom for the problem.
The amount of variability in the data.
The amount of difference between M and μM.
A skewed distribution will remain skewed however it is plotted.
There are limits to the range of scores that can be fitted to a distribution.
A distribution based on sample means will be normal.
There will always be theoretical differences between distributions.
There are no parameter values involved in a t-test.
The t-test is more sensitive to minor differences between sample and population.
With the t-test one can be confident of the normality of the data.
The t-test requires no <known> parameter standard error of the mean.
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