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

Answer:

Then solution as long as n ≥ 56

Step-by-step 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