I need to include measurement uncertainties in this testing process. So I have a theoretical value A

You seem to be talking about inference using confidence intervals. Generally speaking, if the confidence interval does not include a hypthetical value, then the hypothesis is rejected.
More specifically, suppose you have $n=100$ observations from a normal population with unknown mean $\mathrm{\mu <!--\; \mu \; -->}$ and standard deviation $\mathrm{\sigma <!--\; \sigma \; -->}.$ If the sample mean is $\stackrel{¯<!--\; ¯\; -->}{X}=23.4$ and sample standard deviation is $S=3.11,$ then a 95% confidence interval for μ is $\stackrel{¯<!--\; ¯\; -->}{X}\pm <!--\; \pm \; -->1.97S/\sqrt{100}$ or (22.79,24.01). [You can find the formula for this t confidence interval online or in an elementary statistics textbook.]
If you want to test the null hypothesis $H_0:\mathrm{\mu <!--\; \mu \; -->}=20$ against the alternative $H_a:\mathrm{\mu <!--\; \mu \; -->}\ne <!--\; \ne \; -->20,$ then you would reject $H_0$ on the basis of the confidence interval, which does not contain 20 (working at significance level 5%). If you got the confidence from a journal article and trying to test the hypothesis on your own, then this is a reasonable ad hoc inference.
However if you have access to the 100 observations, it is better to do the test yourself. Then you could get a p-value, which would give you a better idea of the strength of the evidence that the population mean is not $\mathrm{\mu <!--\; \mu \; -->}=20.$ You could also check the data to get some idea whether the appropriate statistical method was used. Specifically, you could get an idea whether the population is normal and the observations were chosen at random.