What are the implications of the Central Limit Theorem on statistical testing?
- It asserts that all statistical tests must involve the normal distribution.
- It eliminates the need for statistical testing.
- It guarantees that all results of statistical tests will be accurate.
- It states that sample means will be normally distributed regardless of the shape of the population distribution.
The Central Limit Theorem (CLT) states that, given certain conditions, the mean of a sufficiently large number of independent random variables will be approximately normally distributed, regardless of the shape of the original distribution. This underpins many statistical methods, including hypothesis tests and confidence intervals, which may assume normality of the sampling distribution.
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