Question

The central limit theorem (CLT) predicts that sampling from a normally distributed population results in a...

The central limit theorem (CLT) predicts that sampling from a normally distributed population results in a normally distributed SDM. What would the shape of the SDM be if the population is Skewed? Why?

Homework Answers

Answer #1

As per central limit theorem,

When the population is skewed, the shape of the sampling distribution of mean is normal (or bell) with large sample size (n>30)

since

The central limit theorem states that if you have a population with mean μ and standard deviation σ and large samples from the population with replacement, then the sampling distribution of means will be approximately normally distributed. This will hold true regardless of whether the original population is normal or skewed, provided the sample size is large (n > 30). If the population is normal, then the theorem satisfies even for samples smaller than 30. i.e. n < 30

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The central limit theorem (CLT) is a statistical theory that states that given a sufficiently large...
The central limit theorem (CLT) is a statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population. (true or false?)
Using the central limit theorem, what is the distribution of sample means when the population distribution...
Using the central limit theorem, what is the distribution of sample means when the population distribution is the following? Part (a) rectangular Part (b) normally distributed Part (c) positively skewed Part (d) nonmodal Part (e) multimodal Part (f) negatively skewed
Which of the following is an appropriate statement of the central limit theorem? Select just one....
Which of the following is an appropriate statement of the central limit theorem? Select just one. (1) The central limit theorem states that if you take a large random sample from a population and the data in the population are normally distributed, the data in your sample will be normally distributed.    (2) The central limit theorem states that if you take a large random sample from a population, the data in your sample will be normally distributed. (3) The...
The Central Limit Theorem indicates that in selecting random samples from a population, the sampling distribution...
The Central Limit Theorem indicates that in selecting random samples from a population, the sampling distribution of the the sample mean x-bar can be approximated by a normal distribution as the sample size becomes large. Select one: True False
Question Central Limit Theorem a)According to the Central Limit Theorem, what are the mean and standard...
Question Central Limit Theorem a)According to the Central Limit Theorem, what are the mean and standard deviation of the sampling distribution of sample means? b)A population has a mean ?=1800 and a standard deviation ?=40. Find the mean and standard deviation of the sampling distribution of sample means when the sample size n=100.
You started with a normally distributed population of extraversion scores. You are also interested in depression...
You started with a normally distributed population of extraversion scores. You are also interested in depression scores. The measure of depression is not normally distributed but skewed with a mean of M = 8.08 and a standard deviation of S.D = 6.22. According to the central limit theorem, what would you expect for the mean and standard deviation of the distribution of sample means for samples of a size of 25 from a positively skewed population with M = 8.08...
Why is the Central Limit Theorem considered to be so important for inferential statistics? Consider the...
Why is the Central Limit Theorem considered to be so important for inferential statistics? Consider the mean, standard error, and shape of the sampling distribution of the means in your answer. Also describe the role played, if any, by the underlying or population distribution, sample distribution, and sampling distribution.
Based on the Central Limit Theorem, in which of the following situations will the sampling distribution...
Based on the Central Limit Theorem, in which of the following situations will the sampling distribution of the sample mean NOT be normally distributed? If we sample 14 grocery receipts from a distribution of all receipts with a mean of $128 and a standard deviation of$23. If we sample 50 recent home sales from a distribution of all home sales in the local area with a mean sales price of$315,200 and a standard deviation of $4,700. If we sample 10...
a) What is the Central Limit Theorem? It is always true that as the sample size,...
a) What is the Central Limit Theorem? It is always true that as the sample size, n, increases, the distribution of the sample means will be approximately normally distributed. Explain b) If the underlying population of study is not normally distributed, how large should the sample size be? What if the population is normally distributed ?
§ 1 Central Limit Theorem (CLT) 1. The CLT states: draw all possible samples of size...
§ 1 Central Limit Theorem (CLT) 1. The CLT states: draw all possible samples of size _____________ from a population. The result will be the sampling distribution of the means will approach the ___________________- as the sample size, n, increases. 2. The CLT tells us we can make probability statements about the mean using the normal distribution even though we know nothing about the ______________- 3. The standard error of the mean is the  ___________ of the sampling distribution of the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT