Question

In a random sample of 1000 observations we found that the probability of success to be 48%. The 95% confidence interval for the population proportion is

A.
(0.5 , 0.95)



B.
(0.449 , 0.511)



C.
(0.944 , 0.151)



D.
(0.480 , 0.501)

Answer 1

Standard error of the mean = SEM = $\sqrt{x(N-x)/N^3 }$ = 0.0158

α = (1-CL)/2 = 0.0250

Standard normal deviate for α = Z_α = 1.9600

Proportion of positive results = P = x/N = 0.48

Lower bound = P - (Z_α*SEM) = 0.4490

Upper bound = P + (Z_α*SEM) = 0.5110

B.(0.449 , 0.511)