Question

We wish to study the difference in attitudes between urban residents versus suburban residents in a metropolitan area as these attitudes relate to the proposed construction of a nuclear plant in the area. We obtain a random sample of 80 urban residents and find that 60 of these residents favor the construction of the plant. Independently, we obtain a random sample of 100 suburban residents, finding that 65 of these residents favor construction of the plant. Select the correct expression for the margin of error of the 90% confidence interval for p1 − p2, where p1 denotes the population proportion for urban residents and p2 denotes the population proportion for suburban residents.

a) 1.645 ∙ √ .75 80 + .65 100

b) 1.645 ∙ √ (0.75) 2 80 + (0.65) 2 100

c) 1.645 ∙ √ (.75)(.25) 80 + (.65)(.35) 100

d) 1.960 ∙ √ .75 80 + .65 100

e) 1.960 ∙ √ (0.75) 2 80 + (0.65) 2 100

f) 1.960 ∙ √ (.75)(.25) 80 + (.65)(.35) 100

Answer 1

We have given for the example              
              
x1=60          
n1=80          
              
x2=65          
n2=100          
      
Estimate for sample proportion 1
              
Estimate for sample proportion 2

Z critical value for 90% confidence level =1.645 (by using Z table)

c) 1.645 ∙ √ (.75)(.25) /80 + (.65)(.35) /100