Question

Given that the population proportion is 0.82, the Normal distribution will provide a good approximation to the true sampling distribution of the sample proportion as long as:________.

A) n> 13.
B) n> 30.
C) n> 56.
D) n > 100.

Answer 1

Then solution as long as n ≥ 56

Explanation:

The Normal distribution will provide a good approximation to evaluate proportion tests when the following conditions are met:

n*p₀ > 10

n*q₀ > 10

As p₀ = 0,82 q₀ = 0,18 n = 13 30 56 and 100

We test:

A) n = 13 n*q₀ = 13*0,18 = 2,34 2,34 < 10

B) n = 30 n*q₀ = 30*0,18 = 5,4 5,4 < 10

C) n = 56 n*q₀ = 56 * 0,18 = 10,08

n*p₀ = 56 * 0,82 = 45,92

D) n = 100 n*q₀ = 18

n*p₀ = 82

If we test 55 we find that 55*0,18 = 9,9

Then solution as long as n ≥ 56