Two-tailed T-value?

Question

If you perform a two-tailed T-value test at .05, with 1000 degrees of freedom, and the value returned is 1.962, does that mean that 95% of all data points are likely to occur between 1.962 Standard Deviations above and 1.962 Standard Deviations below your Mean, or that 97.5% of all data points are likely to fall within those Standard Deviations? In other words, is it 2.5% outside each of the 1.962 SD boundaries (total 5%), or is it 5% outside each of the 1.962 SD boundaries (total 10%)? A or B? Similary, if you do the same two-tailed test at .3171, with a t-value of 1.00009, does that mean that 15.87% of your data points are expected to lie outside of each 1 SD boundary or 31.71%? Thank you in advance.

A.
2.5%
_____________1.962

_____________ Mean

_____________1.962

2.5%

B.

5%
_____________1.962

_____________Mean

_____________1.962

5%

Answer 1

Yes, a two-tailed test "splits the difference" on either side of the confidence interval, so that if you have alpha = .05 you'd have half of the error, that is, .025, on either side of the boundaries. This is why two tailed tests are more sensitive than one tailed tests, and harder to prove your reasearch hypothesis. So why not use one tailed tests all the time? Use them only if you are certain that the difference will be directional. Otherwise it's cheating.

Answer 2

Wait for a real stats person for confirmation, but I'm fairly certain it is A--5% total outside of the 1.962 boundaries (2.5% on each side) and that it would be 15.87% for 1 Standard Deviation, but wait for a real stats person for confirmation.

Answer 3

It's 2.5% outside each boundary (option A)