What is Too low of an estimate?

Answer 1

depends on the cost of an error

IF you bet your life on being right, if you bet the family farm, you'd want a monumentally huge range for the estimate, and nothing could really be "too low" or too high. You'd estimate the mean plus or minus a huge number, as large as possible.

But in general, your estimate range depends on the margin of error or the value of alpha. A 99.7 confidence interval has about 3 standard deviations from the mean

then the "too low" estimate would be more than 3 standard deviations below the mean