Question
The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6?
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Answer
Sample size $n=50$
Sample S.D. $s=6.3$
Population S.D. $\sigma=6$
The standard error for sample S.D. is given by
$\begin{aligned} \text { S.E. } & =\sqrt{\frac{\sigma^2}{2 n}} \\ & =\frac{6}{\sqrt{2(50)}} \\ & =\frac{6}{\sqrt{100}} \\ & =0.6\end{aligned}$
Thus standard error for sample S. D = 0.6 .
Sample S.D. $s=6.3$
Population S.D. $\sigma=6$
The standard error for sample S.D. is given by
$\begin{aligned} \text { S.E. } & =\sqrt{\frac{\sigma^2}{2 n}} \\ & =\frac{6}{\sqrt{2(50)}} \\ & =\frac{6}{\sqrt{100}} \\ & =0.6\end{aligned}$
Thus standard error for sample S. D = 0.6 .
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