Question

A random sample of size n = 69 is taken from a population of size N = 971 with a population proportion p = 0.68.

a-1. Is it necessary to apply the finite population correction factor?

Yes or no?

a-2. Calculate the expected value and the standard error of the sample proportion. (Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.)

Expected Value-

Standard Error-

b. What is the probability that the sample proportion is less than 0.57? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

Solution

Given that,

p = 0.68

1 - p = 1 - 0.68 = 0.32

n = 69

N = 971

a-1) Yes, n = 69 > 30 it is necessary to apply the finite population correction factor because finite population correction factor for a sample proportion when the sample size is more than 5% of the population size which is from 5% of population size 971.

a-2) = p = 0.68

=  [p ( 1 - p ) / n] =   [(0.68 * 0.32) / 69 ] = 0.0562

b) P( < 0.57)

= P[( - ) / < (0.57 - 0.68) / 0.0562 ]

= P(z < -1.96)

Using z table,

= 0.0250