Question

In a study of red/green color blindness, 1000 men and 2550 women are randomly selected and tested. Among the men, 86 have red/green color blindness. Among the women, 5 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
The test statistic is =
The p-value is =
Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.01% significance level. A.) No
B.) Yes

2. Construct the 99% confidence interval for the difference between the color blindness rates of men and women.
<(p1−p2)<

Which of the following is the correct interpretation for your answer in part 2?
A. There is a 99% chance that that the difference between the rates of red/green color blindness for men and women lies in the interval
B. We can be 99% confident that that the difference between the rates of red/green color blindness for men and women in the sample lies in the interval
C. We can be 99% confident that the difference between the rates of red/green color blindness for men and women lies in the interval
D. None of the above

Answer 1

1)

A)

p1cap = X1/N1 = 86/1000 = 0.086
p1cap = X2/N2 = 5/2550 = 0.002
pcap = (X1 + X2)/(N1 + N2) = (86+5)/(1000+2550) = 0.0256

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.086-0.002)/sqrt(0.0256*(1-0.0256)*(1/1000 + 1/2550))
z = 14.25

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

B.) Yes

2)

   Here, , n1 = 1000 , n2 = 2550
   p1cap = 0.086 , p2cap = 0.002
  
  
   Standard Error, sigma(p1cap - p2cap),
   SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
   SE = sqrt(0.086 * (1-0.086)/1000 + 0.002*(1-0.002)/2550)
   SE = 0.0089
  
   For 0.99 CI, z-value = 2.58
   Confidence Interval,
   CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
   CI = (0.086 - 0.002 - 2.58*0.0089, 0.086 - 0.002 + 2.58*0.0089)
   CI = (0.061 , 0.107)
  

C. We can be 99% confident that the difference between the rates of red/green color blindness for men and women lies in the interval