Comparing theoretical value with experimental value with measurement uncertainty I need to include measurement uncertainties in this testing process. So I have a theoretical value A that is stated without uncertainty. My measured data gives me this rate value B with uncerainty $\Delta$B.
It used to be validated (B was stated without uncertainty) as if B < const*A then test passes. 
I found this consistensy check that is used for comparing values with uncertainties (if $\mid$A - B$\mid$ $\leq$ $\mid\Delta$A + $\Delta$B$\mid$ is true, then the compared values are consistent with each other within experimental uncertainty), so that would mean that in my situation, I just need to make sure that the difference $\mid$A-B$\mid$ is smaller than $\Delta$B.  1st question - if it doesn't pass this consistency test, are there two not comparable?
And second, what should I do next? How do I compare const*A and B$\pm$$\Delta$B ? I guess the core of the answer will be in overlaping errors, but couldn't have found much on it.
Thanks!
 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 $\mu$ and standard deviation $\sigma.$ If the sample mean is $\bar X = 23.4$ and sample standard deviation is $S = 3.11,$ then a 95% confidence interval for $\mu$ is $\bar X \pm 1.97 S/\sqrt{100}$ 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 $H_0: \mu = 20$ against the alternative
$H_a: \mu \ne 20,$ 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 $\mu = 20.$
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.
