Let us assume two samples, A and B, where A are the results obtained with some standard method, and B are the results obtained with a new method, which is not necessarily more accurate, but has additional advantages (eg: lower cost). 


So I'm interested in testing if B is "as good as" A, using non-inferiority hypothesis testing, i.e. that 


Ho : $A - B >= \delta$


or, equivalently (?)


Ho : $A - \delta >= B$


where $\delta$ is the maximum clinically-acceptable margin of error. 


(Please bear with me if my formulation is not perfect. I'm not a statistician; I'm just a researcher trying to statistically get my way out of a paper bag with minimal damage. Suggestions for improvements are welcome.)


I've seen this hypothesis tested with confidence intervals, which I'm weary of using since my sample size is small. Would it be correct to use Student's t-test to test this hypothesis? If no, why not?


Response to sheldon-cooper:
I'm not sure I fully understand what you mean by "the null hypothesis encompasses many values for the mean of one population"


Assuming that testing for Ho: $A >= B$ can validly be tested using Student's two-sample t-test, how does subtracting $\delta$ from $A$ change the validity of the test? In my perhaps naive understanding, you still get two samples from populations with unknown means that we want to test for equivalence, except that one has been artificially penalized. 



Can t-test be used for non-inferiority hypothesis testing?
Follow-up on my question, after some more research on the question.


The method of using two one-sided two-sample t-tests for clinical equivalence testing is shown in [Schuirmann 1987](https://doi.org/10.1007/BF01068419 "Schuirmann, D.J. A comparison of the Two One-Sided Tests Procedure and the Power Approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics 15, 657–680 (1987)"), and appears relatively standard in bioclinical statistics (at least it is very widely cited). Some preconditions must be respected for the test to be valid (including same sample size for both groups and normal distribution of the data); I will refer you to the article for the complete list.



> 
> Under the normality assumption that has been made, the two sets of one-sided hypotheses will be tested with ordinary one-sided t-tests.
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As the non-inferiority test is only one half of the equivalence testing (In my case, I don't care whether B is superior or simply similar to A), I will assume that the method still holds.


