The formula to calculate the confidence interval is:
\[ X \pm Z \cdot \frac{s}{\sqrt{n}} \]
Where:
A confidence interval is a type of estimate in statistics that shows a possible range of values for an unknown variable or parameter. It provides an interval within which we can be confident that the true value lies, based on the sample data.
Example:
Step 1: Calculate the margin of error:
\[ \text{Margin of Error} = 1.96 \cdot \frac{15}{\sqrt{30}} \approx 5.36 \]
Step 2: Calculate the confidence interval:
\[ \text{Confidence Interval} = [100 - 5.36, 100 + 5.36] = [94.64, 105.36] \]