Central limit theorem (SAMPLING TECHNIQUES PARTT 2)
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What does the Central Limit Theorem (CLT) state about the distribution of sample means?
The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
What is the shape of the sampling distribution of means for large samples regardless of population shape?
It approximates a normal distribution due to CLT.
What is the minimum sample size generally recommended for the Central Limit Theorem to apply?
A sample size of 30 or more (n ≥ 30) is generally considered sufficient for the CLT to apply, though larger samples are preferred for highly skewed populations.
What is the formula for the standard error of the mean?
Standard deviation divided by the square root of sample size.
How does the standard error of the mean relate to population standard deviation and sample size?
The standard error of the mean equals the population standard deviation divided by the square root of the sample size (σ/√n), meaning it decreases as sample size increases.
How does the CLT enable banks to estimate population parameters from sample data?
It assures sample means follow a normal distribution for inference.
What is sampling error in the context of bank audits and statistical sampling?
Sampling error is the difference between the sample statistic and the true population parameter, arising because only a subset of the population is examined rather than all items.
What is the difference between a sampling distribution and a population distribution?
Sampling distribution describes statistics; population distribution describes individual values.
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