Question

Find the margin of error for the 95% confidence interval used to estimate the population proportion.

Answer 1

The formula of the margin of error(E) of the (1- )% confidence interval for the population proportion is as follow:

Where

is the sample proportion

n = sample size

if we have given the number of successes = x

then sample proportion is = = x/n

c = confidence level = 0.95

so that level of significance = = 1 - c = 1 - 0.95 = 0.05

this implies that /2 = 0.05/2 = 0.025

So we want to find such that

Therefore ,

The general excel command to find critical z value is

"=NORMSDIST(probability)"

Here probability = 0.975

So that critical is = "=NORMSINV(0.975)" = 1.96

Here we don't have the values of sample proportion ( ) and n

Let's assume that   = 0.70, and n = 50

So plugging the values in the formula of E, we get

So margin of error = E = 0.127

Note: You can use the given values of sample proportion and n to find the value of E.