Question

Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population standard deviation is 3. Be sure to show that you know the formula and how to plug into it. Also, clearly state the margin of error.

Answer 1

We have been given confidence interval 95%, mean 20 , data set 30 and standard deviation 3.

We will use the formula:
`mean\pm (\sigma)/(√(n))\cdot (z-score)`

Here,
`mean=20,\sigma=3,n=30,z-score=1.96`

Z-score value at 95% confidence interval is 1.96

On substituting the values in the formula to plug the values:

`20\pm(3)/(√(30))\cdot (1.96)`

Now, we have a formula for marginal error:
`z\cdot (\sigma)/(√(n))`

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.