Question

Color blindness, or dyschromatopsia, is a form of genetic deficiency in color perception. The condition is much more prevalent among males than females, pointing to a genetic connection with the X chromosome. The frequency of dyschromatopsia in the Caucasian American male population is about 9%. However, it is thought that this proportion might be smaller among males of other ethnicities. We want to estimate the proportion of Asian American males who are color-blind. How large a sample size do we need in order to obtain a 99% confidence interval with a margin of error no greater than 5%, or 0.05? Use 0.4 for p^^\^.

n = ?

Answer 1

Solution :

Given that,

= 0.4

1 - = 1 - 0.4 = 0.6

margin of error = E = 0.05

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.05)² * 0.4 * 0.6

= 637.03

sample size = n = 638