Question

A poll found that 74% of a random sample of 1029 adults said that they believe in ghosts.

determine the margin of error

Answer 1

Answer)

Given n = 1029

P = 0.74 (74%)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 761.46

N*(1-p) = 267.54

As both are greater than 5,conditions are met so we can use standard nornal z table to estimate the margin of error

Margin of error = z*√p*(1-p)/√n

N = 1029

P = 0.74

Now z is the critical value for different confidence levels

For example, for 95% confidence level, critical value is 1.96

Follow the below mentioned steps to find it

First subtract the confidence level from 1 and then divide the result by 2

(1-0.95)/2 = 0.025

Now from z table, you can see that p(z<-1.96) = p(z>1.96) = 0.025

So, required critical value z is = 1.96

Similarly

Critical value for 90% confidence level is 1.645

And for 99% critical value is 2.58

Just substitute all the values and you will get the margin of error

Margin of error = z*√{p*(1-p)/√n