Question

2. A campaign manager is interested in estimating the proportion of voters who have a favorable view of her candidate. Calculate the minimum sample size needed to be 98% confident that the population proportion is within 5% of the estimate.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 5% = 0.05

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= (2.326 / 0.05)² * 0.5 * 0.5

= 541.02

= 541

n = sample size = 541