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.