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Question:
Discuss how the Central Limit Theorem (CLT) applies when estimating the population mean from a sample, and explain its importance in hypothesis testing.

Solution:
The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's original distribution. This allows statisticians to make inferences about population parameters even when the population distribution is unknown.

In hypothesis testing, the CLT provides a foundation for calculating p-values and confidence intervals, assuming a sufficiently large sample size. It ensures that statistical tests relying on normality, such as z-tests or t-tests, remain robust. This principle simplifies complex data and enables precise conclusions in real-world scenarios.

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