Question

5.70 The ideal number of children. “What do you think is the ideal number of children for a family to have?” A Gallup Poll asked this question of 1020 randomly chosen adults. Slightly less than half (48%) thought that a total of two children was ideal. 20 Suppose that p = 0.48 is exactly true for the population of all adults. Gallup announced a margin of error of ±4 percentage points for this poll. What is the probability that the sample proportion for an SRS of size n = 1020 falls between 0.44 and 0.52? You see that it is likely, but not certain, that polls like this give results that are correct within their margin of error. We say more about margins of error in

Answer 1

n = 1020

p = 0.48

= 0.48

= sqrt(p(1 - p)/n)

     = sqrt(0.48 * (1 - 0.48)/1020)

     = 0.0156

P(0.44 < < 0.52)

= P((0.44 - )/ < ( - )/ < (0.52 - )/)

= P((0.44 - 0.48)/0.0156 < Z < (0.52 - 0.48)/0.0156)

= P(-2.56 < Z < 2.56)

= P(Z < 2.56) - P(Z < -2.56)

= 0.9948 - 0.0052

= 0.9896