Question

8.4

2.)

90% Confidence interval for b.= ____,____

Construct a 90% confidence interval for (P1 – P2) in each of the following situations. a. ny = 400; 21 = 0.64; n2 = 400; P2 = 0.56. b. n1 = 180; f1 = 0.28; n2 = 250; f2 = c. n1 = 100; P1 = 0.47; n2 = 120; f2 = 0.59. = 0.25. a. The 90% confidence interval for (P1 – P2) is (Round to three decimal places as needed.)

90% Confidence interval for c.= ____,____

Answer 1

Confidence interval =
(Pi - P2) + 2* P1 * q P2 * 92 + n1 n2

a)
11
= 400 ,
2
= 400 , $//img.homeworklib.com/questions/28e1c2a0-b288-11eb-882f-0923a640395e.png?x-oss-process=image/resize,w_560$ 1= 0.64, $//img.homeworklib.com/questions/292024b0-b288-11eb-ae58-bfa2d3f54989.png?x-oss-process=image/resize,w_560$ 2 = 0.56 , $//img.homeworklib.com/questions/295c52e0-b288-11eb-82c8-7d9cde331299.png?x-oss-process=image/resize,w_560$ 1 = 1 – $//img.homeworklib.com/questions/29bb8e20-b288-11eb-9311-f7352a6b4900.png?x-oss-process=image/resize,w_560$ 1 = 0.36 , $//img.homeworklib.com/questions/29f830c0-b288-11eb-953d-176cbb53a276.png?x-oss-process=image/resize,w_560$ 2 = 1 – $//img.homeworklib.com/questions/2a350180-b288-11eb-8542-65af756c87c3.png?x-oss-process=image/resize,w_560$ 2 = 0.44

Confidence level = 0.90

α = 1 - 0.90 = 0.1 , 1 - (α/2) = 0.95

So z = 1.645 ----( from z score table )

=

(0.64 -0.56) +1.645 * (0.64 * 0.36) 400 - (0.56 +0.44) 400

= 0.023 and 0.137

90% confidence interval for P1-P2 is 0.023 , 0.137

b)
11
= 180 ,
2
= 250 , $//img.homeworklib.com/questions/28e1c2a0-b288-11eb-882f-0923a640395e.png?x-oss-process=image/resize,w_560$ 1= 0.28, $//img.homeworklib.com/questions/292024b0-b288-11eb-ae58-bfa2d3f54989.png?x-oss-process=image/resize,w_560$ 2 = 0.25 , $//img.homeworklib.com/questions/295c52e0-b288-11eb-82c8-7d9cde331299.png?x-oss-process=image/resize,w_560$ 1 = 1 – $//img.homeworklib.com/questions/29bb8e20-b288-11eb-9311-f7352a6b4900.png?x-oss-process=image/resize,w_560$ 1 = 0.72 , $//img.homeworklib.com/questions/29f830c0-b288-11eb-953d-176cbb53a276.png?x-oss-process=image/resize,w_560$ 2 = 1 – $//img.homeworklib.com/questions/2a350180-b288-11eb-8542-65af756c87c3.png?x-oss-process=image/resize,w_560$ 2 = 0.75

Confidence level = 0.90

α = 1 - 0.90 = 0.1 , 1 - (α/2) = 0.95

So z = 1.645 ----( from z score table )

=$(0.28-0.25)\pm 1.645*\sqrt{\frac{(0.28*0.72)}{180}+\frac{(0.25*0.75)}{250}}$

= -0.041 and 0.101

90% confidence interval for P1-P2 is -0.041, 0.101

c)

11
= 100,
2
= 120 , $//img.homeworklib.com/questions/28e1c2a0-b288-11eb-882f-0923a640395e.png?x-oss-process=image/resize,w_560$ 1= 0.47, $//img.homeworklib.com/questions/292024b0-b288-11eb-ae58-bfa2d3f54989.png?x-oss-process=image/resize,w_560$ 2 = 0.59 , $//img.homeworklib.com/questions/295c52e0-b288-11eb-82c8-7d9cde331299.png?x-oss-process=image/resize,w_560$ 1 = 1 – $//img.homeworklib.com/questions/29bb8e20-b288-11eb-9311-f7352a6b4900.png?x-oss-process=image/resize,w_560$ 1 = 0.53 , $//img.homeworklib.com/questions/29f830c0-b288-11eb-953d-176cbb53a276.png?x-oss-process=image/resize,w_560$ 2 = 1 – $//img.homeworklib.com/questions/2a350180-b288-11eb-8542-65af756c87c3.png?x-oss-process=image/resize,w_560$ 2 = 0.41

Confidence level = 0.90

α = 1 - 0.90 = 0.1 , 1 - (α/2) = 0.95

So z = 1.645 ----( from z score table )

=$(0.47-0.59)\pm 1.645*\sqrt{\frac{(0.47*0.53)}{100}+\frac{(0.59*0.41)}{120}}$

= -0.23 and -0.01

90% confidence interval for P1-P2 is -0.23 , -0.01