Question

A simple random sample size of n = 75 is obtained from a population whose size is N = 10000 and whose population proportion with a specified characteristic is p = 0.8.

a) What is the probability of obtaining x = 63 or more individuals with the characteristic?

b) Construct a 90% interval for the population proportion if x = 30 and n = 150.

Answer 1

a)

b)

Standard error of the mean = SEM = √x(N-x)/N³ = 0.033

α = (1-CL)/2 = 0.050

Standard normal deviate for α = Z_α = 1.645

Proportion of positive results = P = x/N = 0.200

Lower bound = P - (Z_α*SEM) = 0.146

Upper bound = P + (Z_α*SEM) = 0.254