🎢 Hypothesis Testing: Central Limit Theorem🎢

In our last post, we discussed the Sampling Distribution and talked multiple times about the central limit theorem. If you haven’t read that post, then it is advisable to read that post before starting this. Let’s understand it now in detail.

Central Limit Theorem

The central limit theorem says that for any kind of data or regardless of its population distribution if we provided a sufficiently high number of samples (at least more than 30), where each sample is independent of the other and has finite variance, then the sampling distribution becomes a normal distribution.

The Central Limit Theorem holds under three main conditions:

1. Independence: The observations within the sample are independent of each other.
2. Finite Variance: The population from which the samples are drawn must have a finite variance.
3. Sample Size: The sample size should be sufficiently large. While there is no strict rule for the minimum sample size, a commonly used guideline is a sample size of at least 30.

If these 3 conditions are satisfied, then the mean of the sampling distribution of the sample mean will be centered around its population mean.

Central Interval Theorem forms the basis for constructing confidence intervals, performing hypothesis tests, and applying various statistical techniques that rely on the assumption of a normal distribution.

Conclusion

The Central Limit Theorem is a cornerstone of statistical inference, providing a powerful tool for drawing conclusions about population parameters based on sample data. Its ability to transform diverse population distributions into normal sampling distributions allows statisticians to make reliable predictions and decisions in various fields.

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So, this is all from this post, in the next post we will discuss Confidence Interval, Confidence Level, and Margin of Error.

Happy learning!

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