Question

Independent random samples of

n₁ = 700

and

n₂ = 520

observations were selected from binomial populations 1 and 2, and

x₁ = 335

and

x₂ = 378

successes were observed.

(a) Find a 90% confidence interval for the difference (p₁ − p₂) in the two population proportions. (Round your answers to three decimal places.)

Answer 1

We have given,              
              
x1=335          
n1=700          
              
x2=378          
n2=520          
              
Level of significance =   0.1          
Z critical value (by using Z table)=1.645
Estimate for sample proportion 1
              
Estimate for sample proportion 2
  
Confidence interval formula is              


=(-0.293,-0.204)          
              
              
Lower limit for confidence interval=-0.293
              
Upper limit for confidence interval is=   -0.204