Sampling Theory & Sample Mean

8 important questions on Sampling Theory & Sample Mean

What are the key properties of Xˉ\bar{X} ?

Formula:

What is the Central Limit Theorem (CLT)?

When the sample size nn n is large (≥ 30), the distribution of Xˉ\bar{X} is approximately normal, even if the population is not.

What is the Standard Error of the Mean (SE)?

Formula:

It measures how much the sample mean is expected to vary from sample to sample.
Smaller SE → more precise estimate of μ\mu μ.
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What happens when sample size increases?

Table:

What is the difference between σ and s in formulas?

Table:

What is the expected value of the sample mean?

E( Xˉ) = μ

What is the variance of the sample mean?

Formula:

What is the standard deviation of the sample mean?

Formula:

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