Answer:
Check below for the required explanations
Step-by-step explanation:
The population correction factor is given by the formula :
PCF = [(N-n)/(N-1)]^1/2..........(1)
a) When the sample size is smaller than 5% of N. That is n < 0.05N
If n = 0.05N is substituted into the PCF formula, PCF will be approximately 1.
For a value of 1, PCF can be safely ignored.
b) N = 200
i) n = 10% N
n = 0.1 × 200 = 20
Substitute n = 20 into equation (1)
PCF = (200-20)/(200-1)]^1/2
PCF = 0.95
ii) n = 5% N
n = 0.05× 200 = 10
Substitute n = 20 into equation (1)
PCF = (200-10)/(200-1)]^1/2
PCF = 0.98
iii) i) n = 3% N
n = 0.03 × 200 = 6
Substitute n = 20 into equation (1)
PCF = (200-6)/(200-1)]^1/2
PCF = 0.99
iiii) n = 1% N
n = 0.01 × 200 = 2
Substitute n = 20 into equation (1)
PCF = (200-2)/(200-1)]^1/2
PCF = 0.998(approx. =1)
It is noticed that the smaller the sample size, the closer the population correction factor to unity. At 1% of the population, the population correction factor is negligible
