Question

The safety organization conducting the testing in the previous problem was not satisfied with the margin of error. How may helmets would they need to test to reduce the margin of error to 0.03 if we are fairly certain the true proportion is about 40%?

Answer 1

Solution :

Given that,

= 0.40

1 - = 0.60

margin of error = E = 0.03

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 = 1.96

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

= (1.96 / 0.03)² * 0.40 * 0.60

= 1024.43

sample size = 1025