Question

In a study of red/green color blindness, 900 men and 3000 women are randomly selected and tested. Among the men, 84 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 ?_? ???=?_? for the proportions are not equal, ?_?>?_? for the proportion of men with color blindness is larger, ?_?<?_? , for the proportion of men is smaller, and ?_?=?_? for the proportions are equal. )

(a) State the null hypothesis:

(b) State the alternative hypothesis:

(c) The test statistic is  (to two decimal places)

(d) Construct the 99% confidence interval for the difference between the color blindness rates of men and women (round to at least three decimal places). Remember to recalculate the SE, since it is different for CIs and tests.

Answer 1

In a study of red/green color blindness, 900 men and 3000 women are randomly selected and tested. Among the men, 84 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 ?_? ???=?_? for the proportions are not equal, ?_?>?_? for the proportion of men with color blindness is larger, ?_?<?_? , for the proportion of men is smaller, and ?_?=?_? for the proportions are equal. )

1. State the null hypothesis:

Ho: ?_? =?_?

(b) State the alternative hypothesis:

H1: ?_? > ?_?

This is upper tail test

(c) The test statistic is    16.01 (to two decimal places)

	p1	p2	P
	0.0933	0.002	0.0231	p (as decimal)
	84/900	6/3000	90/3900	p (as fraction)
	84.	6.	90.	X
	900	3000	3900	n	Standard error = 0.0057

Data
Hypothesized Difference	0
Group 1
Number of Items of Interest	84
Sample Size	900
Group 2
Number of Items of Interest	6
Sample Size	3000
Intermediate Calculations
Group 1 Proportion	0.0933
Group 2 Proportion	0.0020
Difference in Two Proportions	0.0913
Average Proportion	0.0231
Z Test Statistic	16.0052

(d) Construct the 99% confidence interval for the difference between the color blindness rates of men and women (round to at least three decimal places). Remember to recalculate the SE, since it is different for CIs and tests.

99% CI= (0.066, 0.116)

CI = p1-p2 ± z*se

Standard error of p1-p2= se=

Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level	99%
Intermediate Calculations
Z Value	2.576
Std. Error of the Diff. between two Proportions	0.0097
Interval Half Width	0.0251
Confidence Interval
Interval Lower Limit	0.0663
Interval Upper Limit	0.1164