A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the Northeast and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 1200 northeastern residents and 1280 midwestern residents. 44% of the northeastern residents and 36% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 80% confidence interval for the difference in two proportions. Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval.

a) The 80 % of confidence interval for the difference in two proportions.

(0.055 ,0.105)

b)The critical value that should be used in constructing intervals.

z₀.₂ = 1.28 ( from z-table) at 80 % of level of significance

Step-by-step explanation:

Step :1

Given data the survey included a random sample of 1200 northeastern residents and 1280 midwestern residents.

n₁ = 1200

n₂ = 1280

Given 44% of the northeastern residents reported that they were completely satisfied with their local telephone service.

The first proportion 'p₁' = 0.44

                                  q₁ = 1- p₁ = 1- 0.44 = 0.56

Given 36% of the midwestern residents reported that they were completely satisfied with their local telephone service.

The second proportion 'p₂' = 0.36

                                  q₂ = 1- p₂ = 1- 0.36 = 0.64

Step 2:-

The 80% confidence interval of  p₁- p₂ are

(p₁- p₂ ± zα S.E (p₁- p₂)

where standard error of p₁- p₂

substitute all values ,

on calculation , we get

standard error of (p₁- p₂ ) = 0.0196

Step 3:-

a) The critical value that should be used in constructing intervals.

z₀.₂ = 1.28 ( from z-table) at 80 % of level of significance

Now the 80 % of confidence interval for the difference in two proportions.

(p₁- p₂ ± zα S.E (p₁- p₂)

((0.44-0.36)  - 1.28 (0.0196) , 0.44-0.36  + 1.28 (0.0196))

(0.08 - 0.0250 ,0.08 + 0.0250)

(0.055 ,0.105)

Conclusion:-  

the 80 % of confidence interval for the difference in two proportions.

(0.055 ,0.105)

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation:

ab will be equal to