Which of the following is not a commonly used practice? Choose the correct answer below. A. If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed. B. If the distribution of the sample means is normally distributed, and ngreater than30, then the population distribution is normally distributed. C. The distribution of sample means gets closer to a normal distribution as the sample size n gets larger. D. If the original population is not normally distributed and ngreater than30, the distribution of the sample means can be approximated reasonably well by a normal distribution.

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Аноним Аноним · Answer 1 · 2019-04-12T14:14:42+02:00

Answer:

. B. If the distribution of the sample means is normally distributed, and greater than30, then the population distribution is normally distributed

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joaobezerra joaobezerra · Answer 2 · 2021-10-14T12:42:36+02:00

Using the Central Limit Theorem, it is found that the statement which does not represent a commonly used practice is:

B. If the distribution of the sample means is normally distributed, and n greater than 30, then the population distribution is normally distributed.

The Central Limit Theorem establishes that, for a normally distributed random variable X, the sampling distribution of the sample means with size n can be approximated to a normal distribution.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n greater than 30.

From this, we have that no matter the distribution, for samples of at least 30, the distribution of the sample means is normal.
If the underlying distribution is normal, the sample size is not important.
However, we cannot infer anything about the population given the distribution of the sample means, thus, statement B is false.

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