Question

When constructing an approximate confidence interval for a single mean using a large sample size, we can choose a confidence level that corresponds with the Empirical Rule to determine the critical value, even though our data may not have been sampled from a normal distribution. Explain why we can do this.

Answer 1

This can be the case of the central limit theorem.

It says if a large dataset doesn't follow the normal distribution, then the different means taken for the dataset will follow the normal distribution.

Suppose there is a dataset and we have taken mean m1,m2,m3, and m4. Then, these means will be following the normal distribution.

The definition of central limit theoram is " The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed".

The dataset should be greater than 30.