Question

Assuming that a sample (n = 504) has a sample standard deviation of 2.26, what is the upper bound of a 95% confidence interval if the sample mean is 2.96?

Answer 1

The upper bound would be 3.16.

We find the standard error by dividing the standard deviation by the square root of the sample size:

$\frac{\sigma}{\sqrt{n}}=\frac{2.26}{\sqrt{504}}=\frac{2.26}{22.45}=0.10$

To calculate the margin of error, we multiply the standard error by 2:
0.1(2) = 0.2

For the upper bound, we add this to the mean:
2.96+0.2 = 3.16