Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below. A. The distribution of the sample data will approach a normal distribution as the sample size increases. B. The distribution of the sample means x overbar will, as the sample size increases, approach a normal distribution. C. The mean of all sample means is the population mean mu. D. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.

Question

Social Studies

Lillianna Kaufman

30 October, 19:32

Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below. A. The distribution of the sample data will approach a normal distribution as the sample size increases. B. The distribution of the sample means x overbar will, as the sample size increases, approach a normal distribution. C. The mean of all sample means is the population mean mu. D. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.

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Nickolas Arroyo · Answer 1

D. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.

Explanation:

The central limit theorem is a fundamental probability and statistics theorem. This theorem states that the mean data distribution of a population sample that has a specific purpose will approach a normal distribution as the sample size increases, so the entire sample distribution means that x bar will go as the sample size increase, will approach a normal distribution. With this, we can say that the average of all sample means is the average of the mu population.

This theorem is very useful when it is necessary to analyze factors related to the theory of statistical inferences.