Better Relative Position when both Z Scores are negative

Question

Which Z-Score has the better relative position?

-2.05 or -3.33

Answer 1

Hello Bryan!

I don't know what you mean by "better" relative position.

The Z-scores says to you how many standard deviations from the mean is your value.

A Z-Score of -2.05 is has the cumulative probability of nearly 5% and a Z-score of -3.33 has a cumulative probability of 0.043%.

If you are talking about grades, it would be better to be in the -2.05, because is not that below average than -3.33.

But if you're making hypothesis testing, for example, a Z-score of -3.33, might indicate a very likely alternative hypothesis.