Why does the one-sided T-test reject the Null Hypothesis while the two-sided doesn't? I'm not that familiar with statistics, especially not with T-tests, however I need to apply a T-test for my dataset.
My dataset is basically an observation of productivity over several weeks, where week 1 and 2 are considered as  phase 1 and week 3 as phase 2. I'm comparing if there's a productivity increase between phase 1 and phase 2.
Now, the one-sided T-test rejects the Null hypothesis (with 90%), where the two sided does not reject the Null hypothesis (between 80% and 90%).
Could someone explain to me, what this behavior means and which result I should focus more on?

Let say the significance level $ \alpha $ is 0.05
For a one tailed t-test, the hypothesis is rejected when the test statistic > the 95% quantile (or less than 5% quantile depends on your alternative). While for a two tailed t-test, the hypothesis is rejected when test statistic > the 97.5% qunatile or < 2.5 quantile.
In both case, the type one error is 5% , but when your test statistic lies between 95% and 97.5% quantile, then you will see rejetion for one-tailed test but not two-tailed test.
