I would like to compare potato yield between two varieties. These varieties planted next to each other in the field. From each variety, 12 yield samples were harvested.

I am wondering whether I should use paired t-test or 2-sample t-test for the data analysis.

Paired t-test: The degree of freedom (df) would be n-1 (12-1).

Two sample t-test: The degree of freedom (df) would be 2n-2 (24-2).

I analyzed the data using both tests:

Paired t-test showed that the two variety were statistically not different; Probability > ItI 0.1208

Two sample t-test: Showed that the varieties were statistically significant; Probability > ItI 0.0265

This shows that the 2-sample t-test is statistically more powerful.

I understand that since two sample t-test has higher degree for freedom the corresponding p value would be smaller.

Can someone provide in depth insightful about these two tests and which one I should go for?