Is it true that for an unbiased estimator, the mean of the sampling distribution is very close to, but not always equal to, the true value of the parameter being estimated?
My textbook says that "An unbiased statistic will sometimes fall above or below the true value of the parameter ... because its sampling distribution is centered at the true value, however, there is no systematic tendency to overestimate or underestimate the parameter"; but doesn't this contradict the definition that the expected value of an unbiased estimator is equal to the value of the parameter?
A sample problem:
At a university, students spend an average of 46 minutes per day on Facebook. If all possible SRS of students of size $n=7$ are chosen and a sampling distribution of the sample means is constructed, we would expect the center of that sampling distribution to be ____ 46 minutes.
Would you say exactly equal, or only approximately?