Question

1. In a study of red/green color blindness, 700 men and 2050 women are randomly selected and tested. Among the men, 62 have red/green color blindness. Among the women, 4 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. We can be 99% confident that the difference between the rates of red/green color blindness for men and women lies in the interval
B. 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
C. 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
D. None of the above

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ > 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	62	700	4	2050	0.086620209	0.0066999402	12.928505	<0.0001

99% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	62	700	4	2050	0.086620209	0.010783022	0.058844984	0.11439543

Hence,

1. Test statistic = 12.9285

P - value = 0.0000

Yes; Option B is correct.

2. 99% confidence interval:

0.0588 < (p1 - p2) < 0.1144

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