Question

Suppose an advocacy organization surveys 843843 citizens of Country A and 406406 of them reported being born in another country.​ Similarly, 1919 out of 128128 citizens of Country B reported being​ foreign-born. Find the standard error of the difference in the two proportions.

Answer 1

Solution:

The formula for standard error for difference between two population proportions is given as below:

Standard error = Sqrt[(P1*(1 – P1)/n1) + (P2*(1 – P2)/n2)]

We are given

x1 = 406

x2 = 19

First sample size = n1=843

Second sample size = n2 = 128

First sample proportion = P1 = x1/n1 = 406/843 = 0.481613

Second sample proportion = P2 = x2/n2 =19/128 = 0.148438

Standard error = Sqrt[(P1*(1 – P1)/n1) + (P2*(1 – P2)/n2)]

Standard error = Sqrt[(0.481613*(1 - 0.481613)/843) + (0.148438*(1 - 0.148438)/128)]

Standard error = Sqrt(0.001283691)

Standard error = 0.035828639

Standard error = 0.0358