Let
X
\displaystyle {X}
X
be a random variable with mean 37.4 and standard deviation 2.46. Let
X
‾
\displaystyle \overline{{{X}}}
X
be the sample mean random variable with sample size 33. So,
X
‾
\displaystyle \overline{{{X}}}
X
is the mean of every sample of size 33 taken from
X
\displaystyle {X}
X
.
Sample mean mean is
μ
X
‾
=
\displaystyle \mu_{\overline{{{X}}}}=
μ
X
=
μ
X
‾
\displaystyle \mu_{\overline{{{X}}}}
μ
X
is unknown
and
Sample mean standard deviation (standard error) is
σ
X
‾
=
\displaystyle \sigma_{\overline{{{X}}}}=
σ
X
=
σ
X
‾
\displaystyle \sigma_{\overline{{{X}}}}
σ
X
is unknown
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