In a study of red/green color blindness, 550 men and 2050 women are randomly sel

Question

In a study of red/green color blindness, 550 men and 2050 women are randomly selected and tested. Among the men, 49 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.
(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 10 % significance level.

A. Yes
B. No

(e) Construct the 9090% confidence interval for the difference between the color blindness rates of men and women.

Explanation / Answer

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
HA : p1 - p2 > 0

Hypothesis test results:

90% confidence interval results:

Hence,

a) Null hypothesis: pm - pw = 0

b) Alternative hypothesis: pm - pw > 0

c) Test statistic = 12.841287

d) Yes

e) 90% confidence interval: (0.067095262, 0.10718412)

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