Question

Construct a confidence interval for p1−p2 at the given level of confidence.

x1=377​,

n1=503​,

x2=444​,

n2=589​,

95​% confidence

Answer 1

Solution :

₁ = x₁ / n₁ = 0.75

₂ = x₂ / n₂ = 0.754

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.75 - 0.754

= -0.004

2)

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

= 1.96 (use z table)

Margin of error =   *

=

= 0.0515

3) Required interval is

Point estimate   Margin of error

-0.004   0.037734

(-0.004 - 0.0515 , -0.004 +  0.0515)

(-0.056, -0.048)