Question

1. A pollster wants to construct a 95% confidence interval for the proportion of all U.S. adults who believe that economic conditions are getting better under President Donald Trump. How large a sample should the pollster take so that the estimate is within 3.0% of the true population proportion? [4]

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

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 )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.03)2 * 0.5 * 0.5

= 1067.11

Sample size =1067