Can a Z-Test of Two Sample means in Excel be used to answer two separate hypotheses.

1) Hypothesized Mean Difference=0 (Two-Tailed) (NULL vs Alternate, h_{o}= h_{a})

2) Treatment > Control (One-Tailed)

I am currently doing a Z-Test of Two Sample Means (Control vs Treatment) with Null and Alternate Hypotheses. This is used to determine if there is statistical evidence to indicate a difference between the two means using the Two Tail approach.

Question 1

Can I use the same Z-Test of Two Sample Means output from Excel to Answer Hypothesis 2 above ie Treatment>ControlOR is a t-Test: Two-Sample Assuming Equal Variances the more valid approach.

Question 2

Does it matter if the sample populations vary e.g. n=100 (Treatment) vs n=50 (Control) with either tested hypothesis

Current Logic Hypothesis 1.

If z<z Critical two-tail WE CANNOT REJECT the NULL HYPOTHESIS

And/or if P(Z<=z) two-tail>0.05 WE CANNOT REJECT the NULL HYPOTHESIS

If z>z Critical two-tail WE CAN REJECT the NULL HYPOTHESIS / Accept Alternate Hypothesis

And/or if P(Z<=z) two-tail<0.05 WE CANNOT REJECT the NULL HYPOTHESIS

Proposed Logic Hypothesis 2. Where Treatment > Control else FALSE Treatment < Control

Z-Statistic < Critical One Tail Value Therefore CANNOT REJECT the NULL HYPOTHESIS

Then Check PValue for 1 Tail > 0.05 Therefore CANNOT REJECT the NULL HYPOTHESIS

Z-Statistic > Critical One Tail Value Therefore REJECT the NULL HYPOTHESIS

Then Check PValue for 1 Tail < 0.05 Therefore REJECT the NULL HYPOTHESIS

Thankyou for your time in advance