Question

In an experiment designed to compare the effectiveness of two lotions to relief itching due to poison ivy, 140 volunteer campers were exposed to poison ivy on a small patch on their arm. The volunteers were then randomly assigned one of two lotions: 70 volunteers received lotion A and the other 70 received lotion B. After two minutes, 55 out of 70 of the lotion A group reported total relief from itching. For the lotion B group, 40 out of 70 reported total relief after 2 minutes.

We wish to calculate a 95% confidence interval for the difference (lotion A-lotion B) in the proportion of all campers like these who obtain total relief from itching after two minutes. But first, we must check the conditions.

The LARGE COUNTS condition is easily satisfied.

A. Address the other condition(s).

B. Find a 95% confidence interval for the difference (lotion A-lotion B) in the proportion of all campers like these who obtain total relief from itching after two minutes. Use three places after the decimal   

Answer 1

Ans.

A.

Other assumptions include:

i. Since the volunteers are given lotions randomly , hence the samples are independent.

ii. Since the given data follows binomial proportion distribution , therefore for a large sample it will satisfy the normality assumption.

B.

95% confidence for difference of proportions is given by :

lower limit : ( -) - Z(0.025) *

Upper limit : ( -) + Z(0.025) *

Interval : (0.137, 0.291)