We know that we can make the margin of error smaller (which means that the length of the interval will be smaller) if we reduce our level of confidence. We can also reduce the margin of error by increasing the sample size. We will derive the formula for the sample size n needed so that the confidence interval will have the given margin of error m.

Let m denote margin of error, then

m= z/2(

n

n)

Solve the above equation forn

n(not forn).

You need to show your work to get the credit.

If you now square both sides you will get the required formula.