Question

The results of a recent Pew Research Center survey revealed that 326 of 798 Republicans polled and 107 of 966 Democrats polled said that tax rates on Corporations should be lowered. Based on this survey, estimate with 95% confidence the difference in the percentage of Republicans and Democrats that say tax rates on Corporations should be lowered. Express the estimate both symbolically and verbally.

Answer 1

Solution :

Given that,

n₁ = 798

x₁ = 326

₁ = x₁ / n₁ = 0.409

n₂ =966

x₂ = 107

₂ = x₂ / n₂ = 0.111

1) Point estimate of difference between two proportions

= ₁ -  ₂

= 0.409 - 0.111

= 0.298

2)

= 1.96 (use z table)

Margin of error =   *

=  

= 0.0395

3) Required interval is

Point estimate   Margin of error

0.298   0.0395

0.258 < p1​−p2​ < 0.337

( 0.258 , 0.337 )