TI83 - p-values for less than t test two sample differ by .002 when applying 1-[two-tailed-p-value]

So I thought that a less than p value is equal to 1-[two-tailed-p-value] but on a TI83, I see that this is not the case. The reason I need to know is I am trying to make my own calculator using Apache commons math3 library, their function for a t test gives me a two tailed answer and I also need left and right tailed given that answer.

Below shows what I typed into the calculator and what came out.

On TI83:

x_bar_1 = 9.678571428

Sx1=2.94459418

n1 = 28

x_bar_2 = 6.857142857

Sx2 = 3.86546231

n2 = 28

Not Pooled

For p-value, ≠ is .0034193612

For P-value, < is .9982903194

If the equation was right, (1-[two tailed p value] = less than p), the p value would be .9965806388.

Question:

Is the TI 83 correct?

If it is what equation do I apply in order to find the other two p values?

So I thought that a less than p value is equal to 1-[two-tailed-p-value] but on a TI83, I see that this is not the case. The reason I need to know is I am trying to make my own calculator using Apache commons math3 library, their function for a t test gives me a two tailed answer and I also need left and right tailed given that answer.

Below shows what I typed into the calculator and what came out.

On TI83:

x_bar_1 = 9.678571428

Sx1=2.94459418

n1 = 28

x_bar_2 = 6.857142857

Sx2 = 3.86546231

n2 = 28

Not Pooled

For p-value, ≠ is .0034193612

For P-value, < is .9982903194

If the equation was right, (1-[two tailed p value] = less than p), the p value would be .9965806388.

Question:

Is the TI 83 correct?

If it is what equation do I apply in order to find the other two p values?

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