4. Which of the following is false about the central limit theorem (CLT)?If we take more samples from the original population, the sampling distribution is more likely to be nearly normal.If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardlessof the sample size.As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless ofthe shape of the original population distribution.The CLT states that the sampling distribution will be centered at the true population parameter.X IncorrectThis question refers to the following learning objective(s):Recognizethat the Central Limit Theorem (CLT) is about the distribution of pointestimates, and that given certain conditions, this distribution will benearly normal.In the case of the mean the CLT tells us that if(1a) the sample size is sufficiently large (n > 30) and the data are not extremely skewed or (1b) the population is known to have a normal distribution, and (2) the observations in the sample are independent, thenthe distribution of the sample mean will be nearly normal, centered atthe true population mean and with a standard error ofтеап — ри, SE -Whenthe population distribution is unknown condition (1a) can be checked.

We have to select the false statement regarding central limit theorem.

4. Which of the following is false about the central limit theorem (CLT)? If we take more samples from the original population, the sampling distribution is more likely to be nearly normal. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. The CLT states that the sampling distribution will be centered at the true population parameter.

4. Which of the following is false about the central limit theorem (CLT)? If we take more samples from the original population, the sampling distribution is more likely to be nearly normal. If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless of the sample size. As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of the shape of the original population distribution. The CLT states that the sampling distribution will be centered at the true population parameter.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

4. Which of the following is false about the central limit theorem (CLT)?
If we take more samples from the original population, the sampling distribution is more likely to be nearly normal.
If the population distribution is normal, the sampling distribution of the mean will also be nearly normal, regardless
of the sample size.
As the sample size increases, the sampling distribution of the mean is more likely to be nearly normal, regardless of
the shape of the original population distribution.
The CLT states that the sampling distribution will be centered at the true population parameter.
X Incorrect
This question refers to the following learning objective(s):
Recognize
that the Central Limit Theorem (CLT) is about the distribution of point
estimates, and that given certain conditions, this distribution will be
nearly normal.
In the case of the mean the CLT tells us that if
(1a) the sample size is sufficiently large (n > 30) and the data are not extremely skewed or <br>
(1b) the population is known to have a normal distribution, and <br>
(2) the observations in the sample are independent, <br>
then
the distribution of the sample mean will be nearly normal, centered at
the true population mean and with a standard error of
теап — ри, SE -
When
the population distribution is unknown condition (1a) can be checked.

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