Question

find the sample size needed to give with 99% confidence a margin of error of plus or minus 5% when estimating proportion within plus minus 4% within plus minus 1%

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

a)

margin of error = E = 0.05

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.05)² * 0.5*0.5

= 663.58

sample size = 664

b)

margin of error = E = 0.04

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.04)² * 0.5*0.5

= 1036.84

sample size = 1037

c)

margin of error = E = 0.01

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.01)² * 0.5*0.5

= 16589.44

sample size = 16590