Question

Hello, please review the statement below and determine if the statement is right or not (and why).

Explain the central limit theorem

The central limit theorem states that when there’s a large enough sample size (generally 30 or more) with a finite level of variance, then the mean from all of the samples, from the same population, will be approximately equal to the mean of the population. There are three different components of the theorem. The first is successive sampling from a population, the second is the population distribution, and the third is increasing sample size. The central limit theorem states that when an unlimited number of random samples are taken from a population, the sampling distribution of the means of those samples will become approximately normally distributed with mean μ and standard deviation σ/√ N as the sample size (N) becomes larger, irrespective of the shape of the population distribution.

As sample sizes get bigger, the distributions of means calculated from repeated sampling will approach normality. Leveraging this theorem will enable analysts to take a sample size of a population, then make general conclusions along with leveraging calculating standard deviations to come up with error rates that can guide those that review the data to what variance may exist. In the case of finite populations, a finite correlation factor can be used to further account for potential variance.

The central limit theorem can help different analysts come to conclusions from a sample. For example, marketers can leverage sample data from specific genders, age ranges, and race to come up with different conclusions about their preferences. This information can inform future product enhancements, or how marketing messages are received so that the company can know whether or not to change their advertising approach

Answer 1

Yes, all the statements mentioned above are correct...

It is a statistical theory which generally mentions that if you are given with a sufficiently large or a very large sample size that too from a population with a finite level of variance, then the average of all samples from the same given population will be almost equal to the mean of the given overall population. It generally signifies the shape of the distribution, when we generally try to draw some of the repeated samples from a given set of population. When the sample size increases, the distribution of averages as calculated from these repeated samples will tend towards normality.