CLT and the Normal/Large Sample Condition
In the context of a two-sample t-test for the difference between population means, what is the role of the Central Limit Theorem in satisfying the Normal/Large Sample condition?
It ensures that the sampling distribution of the difference in sample means is approximately normal for large sample sizes, regardless of the underlying population distributions.
It allows us to assume that the population variances are equal, simplifying the calculation of the test statistic.
It guarantees that the individual samples are always normally distributed, regardless of sample size or population shape.
It ensures that the t-distribution closely approximates the z-distribution, eliminating the need for degrees of freedom considerations.
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