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.)
N =Population Size = 650
n = Sample Size = 75
p = Population Proportion = 0.60
q = 1 - p = 0.40
% > 5%
Since sample is more than 5% of the population, it is necessary to apply the finite population correction factor.
Finite Population Correction Factor (FPC) is given by:
the expected value of the sample proportion. = p = 0.60
the standard error of the sample proportion. is given by:
To find P( < 0.50):
Z = (0.50 - 0.60)/0.0566
= - 1.77
By Technology, Cumulative Area Under Standard Normal Curve= 0.0384
the probability that the sample proportion is less than 0.50 = 0.0384
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