Question

Investors are considering funding of new video games. How many people must be surveyed in order to be 95% confident that the estimated percentage is within 4% points of the true population percentage? A.) Assume nothing is known about percentage of people who play video game. B.) Assume that 16% of people play video game.

Answer 1

Solution:

Given that,

a ) = 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= (1.960 / 0.04)² * 0.5 * 0.5

= 600.25

= 600

n = sample size = 600

b ) = 0.16

1 - = 1 - 0.16 = 0.84

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= (1.960 / 0.04)² * 0.16 * 0.84

= 322.69

= 323

n = sample size = 323