I am having some problems when I need to calculate the test $Z$. Suppose I got a value, by a measurement, of $x = 3.44433$ with uncertainty $0.00003$. And, for example, it is given to me a "theoretical/standard" value of this $x$, let's say it is $3.44$
How can I see, if both are compatible? I mean, the test $Z$ says that if $|Z| = \frac{x-\mu}{\delta} < 3$, then they are compatible.
The problem is, here, in the formula, should I use $x-\mu = 0.00433$, as a normal subtraction, or should I use $x-\mu = 0.00$, since the rules of significant figures claim that in the subtraction we just consider the resultant number until the last decimal of the number which has lesser number of significant figures?
Now, using the first method gives an incompatibility, and the second method, compatibility. So what is right?