To find the estimated standard error (SE) of the sample mean given the sample size (N) and the sample standard deviation (s), we can use the formula for the standard error of the mean:
[tex]\[ SE = \frac{s}{\sqrt{N}} \][/tex]
Here, [tex]\( s \)[/tex] is the sample standard deviation, and [tex]\( N \)[/tex] is the sample size.
1. Given:
- Sample size [tex]\( N = 712 \)[/tex]
- Sample standard deviation [tex]\( s = 1.67 \)[/tex]
2. We need to calculate the square root of the sample size [tex]\( N \)[/tex]:
[tex]\[ \sqrt{N} = \sqrt{712} \approx 26.678 \][/tex]
3. Next, we divide the sample standard deviation [tex]\( s \)[/tex] by the square root of the sample size:
[tex]\[ SE = \frac{1.67}{26.678} \][/tex]
4. Performing the division, we get:
[tex]\[ SE \approx 0.06258589603115443 \][/tex]
Therefore, the estimated standard error is approximately [tex]\( 0.06258589603115443 \)[/tex].
