Which of the following is not true about the standard error of a statistic?
a. the standard error measures, roughly, the average difference between the statistic and the population parameter.
b. the standard error is the estimated standard deviation of the sampling distribution for the statistic.
c. the standard error can never be a negative number.
d. the standard error increases as the sample size(s) increases.

Only option d is not true

Step-by-step explanation:

Given are four statements about standard errors and we have to find which is not true.

A. The standard error measures, roughly, the average difference between the statistic and the population parameter.

-- True because population parameter is mean and the statistic are the items.  Hence the differences average would be std error.

B. The standard error is the estimated standard deviation of the sampling distribution for the statistic.

-- True the sample statistic follows a distribution with standard error as std deviation

C. The standard error can never be a negative number. -- True because we consider only positive square root of variance as std error

D. The standard error increases as the sample size(s) increases

-- False.  Std error is inversely proportional to square root of n.  So when n  decreases std error increases

thats not a system of equations, that is a solution