Suppose that the population distribution of a variable (X) has a mean (μ) and a standard deviation (σ). If you randomly draw an infinite number of samples from the population, and if the sample size (N) is big enough, then the distribution of the sample means (X) has a normal distribution with a mean (μx = μ) and a standard deviation (σx =σ/√N).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 8E
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What does this explain? Sampling frame, Measure of central tendency, Sampling Distribution, Central Limit Theorem, or Confidence interval estimation

 

 

Suppose that the population distribution of a variable (X) has a mean (μ)
and a standard deviation (σ). If you randomly draw an infinite number of
samples from the population, and if the sample size (N) is big enough, then
the distribution of the sample means (X) has a normal distribution with a
mean (μx = μ) and a standard deviation (σx =σ/√N).
Transcribed Image Text:Suppose that the population distribution of a variable (X) has a mean (μ) and a standard deviation (σ). If you randomly draw an infinite number of samples from the population, and if the sample size (N) is big enough, then the distribution of the sample means (X) has a normal distribution with a mean (μx = μ) and a standard deviation (σx =σ/√N).
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