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27.02.2020 •
Mathematics
Which of the following SRS designs will give the most precision (smallest standard error) for estimating a population mean? Assume that each population has the same value of the population variance S^2?
1) An SRS of size 400 from a population of size 4000
2) An SRS of size 30 from a population of size 300
3) An SRS of size 3000 from a population of size 300,000,000
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Ответ:
Design 3: An SRS of size 3000 from a population of size 300,000,000
Step-by-step explanation:
To check the SRS designs will give the most precision (smallest standard error) for estimating a population mean, we'll make use of the following formula:
V(y) = S²/n( 1 - n/N)
Where S² is a constant for the three SRS designs
Check the first design
n = 400
N = 4000
So, V(y) = S²/400 (1 - 400/4000)
V(y) = S²/400(1 - 0.1)
V(y) = 0.0025S²(0.9)
V(y) = 0.00225S²
V(y) = 2.25S²E-3
The second design
n = 30
N = 300
So, V(y) = S²/30 (1 - 30/300)
V(y) = S²/30(1 - 0.1)
V(y) = S²/30(0.9)
V(y) = 0.03S²
V(y) = 3S²E-2
The third design
n = 3,000
N = 300,000,000
So, V(y) = S²/3,000 (1 - 3,000/300,000,000)
V(y) = S²/3,000(1 - 0.00001)
V(y) = S²/3,000(0.99999)
V(y) = 0.00033333
V(y) = 3.33S²E-4
Ответ:
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