In a study of red/green color blindness, 600 men and 2150 women are randomly selected and tested. Among the men, 55 have red/green color blindness. Among the women, 6 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.
(Note: Type $``p\_m''$ for the symbol $p_m$ , for example $p\_m \; not = p\_w$ for the proportions are not equal, $p\_m > p\_w$ for the proportion of men with color blindness is larger, $p\_m < p\_w$ , 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 1 % significance level.

A. Yes
B. No

(e) Construct the $99$% confidence interval for the difference between the color blindness rates of men and women.