Question

Eric Garcetti, the mayor of Los Angeles, wants to estimate the percentage of all residents in favor of lifting the safer-at-home order and returning to normal life. He wants to provide a margin of error of no more than 1.8% with 99% confidence. How many residents should he sample to achieve this?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 1.8% = 0.018

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.018)2 * 0.5 * 0.5

=5120.19

Sample size = 5121

when you have z value 2 decimal than Z/2 = 2.58 =n=5136.11=5137