Question

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 ?

Homework Answers

Answer #1

(a) The central limit theorem says that the mean of samples are normally distributed no matter what the distribution they are taken from.

Mathematically,

Let Y = X1 + X2 + X3 +.........

Define,

As n approaches infinity, Zn approaches the standard normal distribution.

By the definition, As n approaches infinity, Zn approaches the standard normal distribution. Hence it is always true (and in fact desirable) that as the sample size increases, the distribution of sample means will be approximately normally distributed.

(b) As a rough guideline, if the population is not normally distributed then it is suggested to have a sample size of at least 30 for a good approximation.

If the population is normally distributed then all the sample points would be on a normal distribution curve. So regardless of sample size, sample would be normally distributed.

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
Which one of the following statements is true? A. The Central Limit Theorem states that the...
Which one of the following statements is true? A. The Central Limit Theorem states that the sampling distribution of the sample mean, y , is approximately Normal for large n only if the distribution of the population is normal. B. The Central Limit Theorem states that the sampling distribution of the sample mean, y , is approximately Normal for small n only if the distribution of the population is normal. C. The Central Limit Theorem states that the sampling distribution...
True or False. The central limit theorem states that as the number of sample size increases,...
True or False. The central limit theorem states that as the number of sample size increases, the distribution of the sample means approximates to a normal distribution.
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.
The Central Limit Theorem says that when sample size n is taken from any population with...
The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true? The distribution of the sample mean is approximately Normal. The standard deviation is equal to that of the population. The distribution of the population is exactly Normal. The distribution is biased.
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 suggests that as the sample size increases the distribution of the sample...
The Central Limit Theorem suggests that as the sample size increases the distribution of the sample averages approaches a normal distribution, regardless of the nature of the distribution of the variable itself. true or false
What is wrong with the following statement of the central limit theorem? Central Limit Theorem.  If the...
What is wrong with the following statement of the central limit theorem? Central Limit Theorem.  If the random variables X1, X2, X3, …, Xn are a random sample of size n from any distribution with finite mean μ and variance σ2, then the distribution of will be approximately normal, with a standard deviation of σ / √n.
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
According to the central limit theorem, if a sample of size 81 is drawn from a...
According to the central limit theorem, if a sample of size 81 is drawn from a population with a variance of 16, the standard deviation of the distribution of the sample means would equal _______. .98 .44 .68 .87 .75
Which of the following statements is not consistent with the Central Limit Theorem? 1. The Central...
Which of the following statements is not consistent with the Central Limit Theorem? 1. The Central Limit Theorem applies to non-normal population distributions. 2. The standard deviation of the sampling distribution will be equal to the population standard deviation. 3. The sampling distribution will be approximately normal when the sample size is sufficiently large. 4. The mean of the sampling distribution will be equal to the population mean.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT