Question

A telephone poll of 1000 adult Americans was reported in an issue of a magazine. One of the questions asked was "[How much are] you worried about the quality of education in our schools?" Suppose 64% responded "a lot". We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

Which distribution should you use for this problem? (Round your answers to three decimal places.)

P' ~ N ( ? , ? )

Answer 1

Solution

Given that,

p = 0.64

1 - p = 1 - 0.64 = 0.36

n = 1000

np > 10 and n(1 - p) > 10

1000 * 0.64 = 640 > 10 and 1000 * 0.36 = 360 > 10

The sampling distribution of the is approximately normal

N ( 0.64, 0.015 )

= p = 0.64

  [p ( 1 - p ) / n] = [(0.64 *0.36) / 1000 ] = 0.015