Question

A random sample of size n = 75 is taken from a population of size N = 650 with a population proportion p = 0.60.

Is it necessary to apply the finite population correction factor? Yes or No?

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.)

What is the probability that the sample proportion is less than 0.50? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

(a)

N =Population Size = 650

n = Sample Size = 75

p = Population Proportion = 0.60

q = 1 - p = 0.40

Since

% > 5%

Since sample is more than 5% of the population, it is necessary to apply the finite population correction factor.

So,

Correct option:

Yes

(b)

Finite Population Correction Factor (FPC) is given by:

(i)

the expected value of the sample proportion. = p = 0.60

(ii)

the standard error of the sample proportion. is given by:

(c)

To find P( < 0.50):

Z = (0.50 - 0.60)/0.0566

= - 1.77

By Technology, Cumulative Area Under Standard Normal Curve= 0.0384

So,

the probability that the sample proportion is less than 0.50 = 0.0384