Precision of the Mean

Standard error scales with the inverse square root of sample size.

The population standard deviation is 4.

1. 1. Recover standard deviation

   Variance $16$ means the population standard deviation is $4$.

2. 2. Scale by sample size

   Divide by $\sqrt{64}$.

   $$\mathrm{SE}(\bar{X})=\frac{\sigma }{\sqrt{n}}=\frac{4}{8}=0.5$$

Answer: 0.5