Question

Construct a confidence interval for at the given level of confidence.
x₁=29​, n₁=248​, ​x₂=31, n₂=298​, ​95% confidence.

Answer 1

Solution :

Given that,

₁ = x₁ / n₁ = 0.117

₂ = x₂ / n₂ = 0.104

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.117 - 0.104

= 0.013

2)

Our aim is to construct 95% confidence interval.

= 1.96 (use z table)

Margin of error =   *

=

= 0.053

3) Required interval is

Point estimate   Margin of error

0.013   0.053

(0.013 - 0.053 , 0.013 +  0.053)

(-0.040 , 0.066)