Question

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.16
(b) there is no preliminary estimate for p

Answer 1

We have given,
Margin of error =E=0.1
Level of significance =   1-0.95=0.05
Z critical value is (by using Z table) =1.96
Sample size formula is                   

a) Preliminary estimate for proportion (Known) = 0.16

=51.63                  
                                      
                  
Therefore , sample size approximately will be 52

b)
Preliminary estimate for proportion (Not Known) = 0.5

=96.04

Therefore , sample size approximately will be 97