Answer:
We have been given confidence interval 95%, mean 20 , data set 30 and standard deviation 3.
We will use the formula: [tex]mean\pm \frac{\sigma}{\sqrt{n}}\cdot (z-score)[/tex]
Here,[tex]mean=20,\sigma=3,n=30,z-score=1.96[/tex]
Z-score value at 95% confidence interval is 1.96
On substituting the values in the formula to plug the values:
[tex]20\pm\frac{3}{\sqrt{30}}\cdot (1.96)[/tex]
Now, we have a formula for marginal error:[tex]z\cdot \frac{\sigma}{\sqrt{n}}[/tex]
Marginal error means your answer will be within that percentage only.
Say you have 3% marginal means your value will be within 3% real population 95% of the time.
