Question

Suppose we know that a confidence interval for a population proportion is (0.572,0.662), with a sample proportion of p′=0.617. What is the margin of error?

Answer 1

Answer:  0.045

Explanation:

The sample proportion 0.617 is at the exact midpoint of the interval from  0.572 to 0.662

We can confirm this by applying the midpoint formula.

The distance from the center (0.617) to either endpoint will be the margin of error. In other words, it is half the width of the confidence interval

L = lower boundary of confidence interval = 0.572

C = center of confidence interval = 0.617

U = upper boundary of confidence interval = 0.662

We have three methods to find the confidence interval

• margin of error = U - C = 0.662-0.617 = 0.045
• margin of error = C - L = 0.617 - 0.572 = 0.045
• margin of error = (width)/2 = (U-L)/2 = (0.662-0.572)/2 = 0.045

Each yielding the same result of 0.045

With the third method, you don't need to know the center of the confidence interval.