Question

A sample of 1500 people from a certain industrial community showed that 800 people suffered from a lung disease. A sample of 1000 people from a rural community showed that 300 suffered from the same lung disease. Assume these two proportions give good estimates of population proportions, respectively. Find the probability that the difference of the proportions (industrial - rural) is greater than 0.2 if two samples of size 150 and 100 are drawn from the two populations, respectively.

Answer 1

The probability that the difference of the proportions (industrial - rural) is greater than 0.2 is 0.7054

Explanation:

Solution

Given that:

n₁ = 1500

x₁ = 800

p₁ =800/1500 =0.533

q₁ = 1- 0.533 = 0.467

Thus,

n₂ =1000

x₂ = 300

p₂ = 300/1000 = 0.3

q₂ = 1-0.3 =0.7

So,

p₁ - p₂ = 0.533 - 0.3

=0.233

Now,

SE (p₁ - p₂ ) =√0.533 * 0467/150 + 0.3 * 0.7/1000

=0.0613

So,

p ( p₁ - p₂ > 0.2

= p ( Ƶ > 0.2 - 0.233/0.0613

p = ( Ƶ > - 0.54)

= 0.7054