91 Construct the 995 confidence interval for the difference

9.1

Construct the 99.5% confidence interval for the difference p 1 - p 2 when x 1 = 40, n1 = 70, x 2 = 15. and n 2 = 50 Round the answers to three decimal places. A 99.5% confidence interval for the difference between the two proportions is [ ]

Solution

From the given values we find p1-p2 from sample and try to find std error using

pooled variance then divide by n1+n2 and take square root

Lower bound = 0.2714-0.1248 = 0.1466

Upper bound = 0.2714+0.1248 = 0.3962

Confidence interval for 99.5 % for difference between two proportions is

(0.1466, 0.3962)

i.e. 0.1466<p1-p2 <0.3962

NOte (Z value has been used for 99.5% confidence interval)

	Sample I	Sample II	Total
x	40	15	55
n	70	50	125
p =propor	0.5714	0.3	0.44
p1-p2	0.2714
std error^2	p(1-p)/n	0.0020
std error		0.044398198
99.5% z	-2.81	2.81
Margin of	-0.12476	0.124758937
error