Significance (t-statistic)

I'm not sure how to answer this one:


You are testing Ho: mu = 0 against Ha: mu (does not equal) 0 based on an SRS of 20 observations from a Normal population. What values of the t statistic are statistically significant at the alpha = 0.005 level?

Is the answer t > 2.861 or is it 3.174 > t > 2.539

or am I totally off on both tries?!

Thanks in advance!


TS Contributor
With a 2-tailed test, as this is, any value of t > 3.174 or t < -3.174 is significant at the .005 level of significance.
I was wondering why it is t > 3.174 and not t > 2.861 as 2.861 is the value that falls below alpha .005 and 3.174 is the value that is below .0025.

Thanks in advance :)


TS Contributor
Those are upper-tail probabilities only.....for a two-tail probability the rejection region needs to be split in half between the lower and upper tails, thus pushing the t value higher.