Question

A common Gallup poll question asks Americans whether they would like to see handguns banned. A recent poll indicated that 27% of those polled by Gallup said “Yes.” Calculate the margin of error for that figure, assuming a 95% confidence level and a sample size of 1,000 respondents. (Input the number in percent form with 1 decimal place and no percent sign)

Answer 1

Solution :

Given that,

n = 1000

Point estimate = sample proportion = = 0.27

1 -   = 1-0.27 =0.73

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.27*0.73) / 1000)

E = 0.028

Margin of error = E =2.8