In a study of red/green color blindness. 1000 men and 2800 women are randomly se

Question

In a study of red/green color blindness. 1000 men and 2800 women are randomly selected and tested Among the men. 85 have red/green color blindness. Among the women, 6 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.05% significance level? Construct the 95% confidence interval for the difference between the color blindness rates of men and women Which of the following is the correct interpretation for your answer in part 2?

Explanation / Answer

1.

Formulating the hypotheses          
Ho: p1 - p2   <=   0  
Ha: p1 - p2   >   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.085      
p2 = x2/n2 =    0.002142857      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.008862204      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    9.349495843   [ANSWER, TEST STATISTIC]

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As significance level =    0.0005   , then the critical z is  
          
zcrit =    3.290526731      
          
Also, the p value is          
          
P =    4.40332*10^-21       [ANSWER, P VALUE]

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As z > 3.29, and P < 0.0005, we    REJECT THE NULL HYPOTHESIS.      

Hence, YES, THERE IS SUFFICIENT EVIDENCE. [ANSWER]

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2.

For the   95%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.025      
z(alpha/2) =    1.959963985      
Margin of error = z(alpha/2)*sd =    0.017369601      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.065487541      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.100226744      
          
Thus, the confidence interval is          
          
(   0.065487541   ,   0.100226744 ) [ANSWER]

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OPTION A: We can be 95% confident that the difference between the rates of ref/green color blindness for men and women lies in the interval. [CONCLUSION]

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