Question

In the equation for a confidence interval, the sample size is located in the denominator underneath the radical sign. What happens to the value of the expression under the radical sign as the sample size increases?

Answer 1

Explanation:

Given that in the equation for a confidence interval, the sample size is located in the denominator underneath the radical sign.

In hypothesis testing we have

Confidence interval = Mean ±Margin of error

= Mean±Z critical*std dev/sqrt n

Thus we find that whenever n increases, sqrt of n increases, margin of error decreases and as a result we find that whenever sample size increases then sqrt n also increases which in turn reduces the wirth of confidence interval.