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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]