Respuesta :
Answer:
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.
Using the Central Limit Theorem, it is found that the statement is True.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
- For a skewed variable, it is valid for sample sizes of at least 30.
In the context of this problem, the sample size restriction is only for non-normal underlying distribution, hence the statement is True.
A similar problem is given at https://brainly.com/question/14099217
