Question

A CBS News/New York Times poll found that 329 out of 763 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% accuracy. Round your answers to three decimal places. 

Answer 1

Using Normal approximation:-

Standard error of the mean = SEM = √x(N-x)/N³ = 0.018

α = (1-CL)/2 = (1-0.88)/2 = 0.060

Standard normal deviate for α is Z_α = 1.555

Proportion of positive results = P = x/N = 0.431

Lower bound = P - (Z_α*SEM) = 0.403

Upper bound = P + (Z_α*SEM) = 0.459