Question

In a study of red/green color blindness, 950 men and 2550 women are randomly selected and tested. Among the men, 85 have red/green color blindness. Among the women, 7 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
(Note: Type ‘‘p_m′′‘‘p_m″ for the symbol pmpm , for example p_mnot=p_wp_mnot=p_w for the proportions are not equal, p_m>p_wp_m>p_w for the proportion of men with color blindness is larger, p_m<p_wp_m<p_w , for the proportion of men is smaller. )

(a) State the null hypothesis:

(b) State the alternative hypothesis:

(c) The test statistic is

(d) Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women? Use a 5 % significance level.

A. Yes
B. No

(e) Construct the 95% confidence interval for the difference between the color blindness rates of men and women.___ <(pm−pw)<___

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	85	950	7	2550	0.086728586	0.006081039	14.262133	<0.0001

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	85	950	7	2550	0.086728586	0.0093182345	0.068465182	0.10499199

Hence,

a) Null: p_m = p_w

b) Alternative: p_m > p_w

c) Test statistic = 14.2621

d) Yes

e) 95% confidence interval:

0.0685 < (pm−pw) < 0.1050