Is the statement below true or false? The distribution of the sample mean, x overbar , will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size.

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Mathematics

Coleman Villegas

28 September, 12:23

Is the statement below true or false? The distribution of the sample mean, x overbar , will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size.

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Answers (1)

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Martin Baker · Answer 1

The given statement " The distribution of the sample mean, x-bar, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size " is True.

Step-by-step explanation:

Given statement is " The distribution of the sample mean, x overbar , will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size".

To check whether the given statement is true or not : The distribution of the sample mean, x-bar, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size is True. The standard error of the mean is divided into half, then the sample size must be doubled.

∴ The given statement is true.