Question

In a study of red/green color blindness, 750 men and 2500 women are randomly selected and tested. Among the men, 66 have red/green color blindness. Among the women, 8 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 90% confidence interval for the difference between the color blindness rates of men and women.

<(pm−pw)<<(pm−pw)<

Answer 1

Answer:. In a study of red/green color blindness, 750 men and 2500 women are randomly selected and tested. Among the men, 66 have red/green color blindness. Among the women, 8 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.

Solution:

The hypothesis test:

a) Null hypothesis, Ho: p_m = p_w

b) Alternative hypothesis, Ha: p_m > p_w

c) The test statistic is: