Difference between parameter and estimate
If the value of a parameter specified by the null hypothesis (e.g. a population proportion, π0) is close to the corresponding sample statistic (e.g. the sample proportion, p) then there is no reason to doubt the null hypothesis. However if they are far apart, the data are not consistent with the null hypothesis and we should conclude that the alternative hypothesis holds.
A large distance between the estimate and hypothesized value gives evidence against the null hypothesis.
Statistical distance
To help assess this difference, we express it as a number of standard errors since we know from the 70-95-100 rule of thumb that that 2 (standard errors) is a large distance, 3 is a very large distance, and 1 is not much.
For a proportion, the number of standard errors is
In general, the statistical distance of an estimate to a hypothesised value of the underlying parameter is
Values more than 2, or less than -2, suggests that the hypothesized value is wrong. However if z is close to zero, p is reasonably close to π0 and we should not doubt the null hypothesis.