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)