Question

In a study of red/green color blindness, 650 men and 2950 women are randomly selected and tested. Among the men, 60 have red/green color blindness. Among the women, 9 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.

<(pm−pw)<<(pm−pw)<

Answer 1

(a) The null hypothesis

H0: p_m = p_w

(b) The alternative hypothesis

Ha: p_m > p_w

(c) Test statistic

Q = 1-P= 0.9808

= 15.02

The test statistic is , z =15.02

(d) P value for z =15.02 is

P value is less than 0.0001

Since P value < 0.10

the result is significant

We reject H0

YES , There is sufficient evidence to support the claim that men have higher rate of red green color blindness than women

(e) For 90% confidence

zc = 1.65

90% confidence interval for difference between color blindness rate for men and women is

= (0.0795, 0.0991)

Therefore,

90% confidence interval for difference between color blindness rate for men and women is

0.0795 < p_m - p_w < 0.0991