Color blindness, or dyschromatopsia, is a form of genetic deficiency in color pe
ID: 3133212 • Letter: C
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 8%. 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 3%, or 0.03? Use 0.3 for p^^^.
Explanation / Answer
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.005
Using a table/technology,
z(alpha/2) = 2.575829304
Also,
E = 0.03
p = 0.3
Thus,
n = 1548.14254
Rounding up,
n = 1549 [ANSWER]