Question

1. In a study of red/green color blindness, 950 men and 2300 women are randomly selected and tested. Among the men, 83 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 0.05% significance level?

A. Yes

B. No

2. Construct the 95% 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. We can be 95% confident that the difference between the rates of red/green color blindness for men and women lies in the interval

B. We can be 95% 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. There is a 95% chance that 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

a)

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

p1cap = X1/N1 = 83/950 = 0.0874
p1cap = X2/N2 = 5/2300 = 0.0022
pcap = (X1 + X2)/(N1 + N2) = (83+5)/(950+2300) = 0.027

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.0874-0.0024)/sqrt(0.027*(1-0.027)*(1/950 + 1/2300))
z = 13.6

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

yes, 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

b)

Here, , n1 = 950 , n2 = 2300
p1cap = 0.0874 , p2cap = 0.0022

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.0874 * (1-0.0874)/950 + 0.0022*(1-0.0022)/2300)
SE = 0.0092

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.0874 - 0.0022 - 1.96*0.0092, 0.0874 - 0.0022 + 1.96*0.0092)
CI = (0.0672 , 0.1032)

0.0672 < p1 - p2 < 0.1032

A. We can be 95% confident that the difference between the rates of red/green color blindness for men and women lies in the interval