Question

We wish to compare the prevalence of parasites in Mediterranean fish to the prevalence of parasites in Atlantic fish. In the Mediterranean Sea 500 brill were captured and dissected; 150 were found to contain parasites   In the Atlantic 200 brill were captured and dissected; 40 were found to have parasites. In what follows, let p₁ denotes the infestation rate for the Mediterranean brill and p₂ denote the infestation rate for the Atlantic brill. Find the margin of error for the 90% confidence interval for the difference p₁   - p_2..

0.12

0.07

0.04

0.06

0

Answer 1

Solution :

Given that,

n₁ = 500

x₁ = 150

₁ = x₁ / n₁ = 0.3

n₂ =200

x₂ = 40

₂ = x₂ / n₂ = 0.2

Our aim is to construct 90% confidence interval.

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05 and 1- /2 = 0.950

= 1.645 (use z table)

Margin of error =   *

=  

= 0.06

The margin of error for the 90% confidence interval for the difference p₁   - p_{2. is 0.06}