state the null and alternative hypothesis, find the test statistic.

Question

In a study of red/green color blindness, 1000 men and 2850 women are randomly selected and tested. Among the men, 90 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″ for the symbol pm , for example p_mnot=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) Construct the 99% confidence interval for the difference between the color blindness rates of men and women.


? <(pm−pw)< ?

Answer 1

Null hypothesis: Ho p_m = p_w

 

Alternative hypothesis: Ha p_m > p_w

 

p_m = 90/1000 = 0.09

p_w = 8/2850 =   .00281

 

Test statistics = 15.06

 

99% Confidence Interval = (.06374, .11064)

 

This means that proportion of mean with color blindness are greater than the proportion of women with color blindness.