Financial Risk Manager Part 1
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From a population of 10,000 observations, a researcher chooses a sample of 1,000. If the population's standard deviation is 100, then what is the standard error of the mean?
Other
Community
NNikitesh
A
0.1
B
3.16
C
27.6
D
0.01
Explanation:
The standard error of the sample mean is calculated as:
Standard Error = Population Standard Deviation / √Sample Size
Given:
- Population standard deviation (σ) = 100
- Sample size (n) = 1,000
Calculation: √1,000 ≈ 31.6228 Standard Error = 100 / 31.6228 ≈ 3.16228 ≈ 3.16
Why other options are incorrect:
- A (0.1): This would be 100/1,000, which is incorrect because we need to divide by the square root of the sample size, not the sample size itself.
- C (27.6): This is too large and doesn't correspond to any standard calculation.
- D (0.01): This would be 100/10,000, which incorrectly uses the population size instead of the sample size.
Key Concept: The standard error measures the precision of the sample mean as an estimate of the population mean. As sample size increases, the standard error decreases, making the sample mean a more precise estimate of the population mean.
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