The standard error of an estimator ϕ is it's standard deviation, given by
σϕ = √𝑉(ϕ). If the standard error involves unknown parameters that can be
estimated, substitution of those values into σϕ produces an estimated standard
error.
2
σ
The standard error of the sample mean is σx̄ =√ and since σ is unknown, we
𝑛
may replace it by the sample standard deviation s:
Estimated standard error:
𝑠
= 0.284
√𝑛
=
0.284
√10
= 0.0898
0.0898
Notice that the standard error is about 0.2 (
) percent of the sample mean,
41.924
implying that we have obtained a relatively precise point estimate of thermal
conductivity.
If we can assume that thermal conductivity is normally distributed, 2 times the
standard error is 0.1796.
Then we would be highly confident that the true mean thermal conductivity is
with the interval 41.294 ± 0.1796 or between 41.1144 and 41.4736.
Mean Square Error