Question

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 of the sample mean, y , is approximately Normal for small n regardless of the distribution of the population.

D. The Central Limit Theorem states that the sampling distribution of the sample mean, y , is approximately Normal for large n regardless of the distribution of the population.

Please Explain and show work if possible. Thank you!

Homework Answers

Answer #1

First of all, the central limit theorem assumes the sample size to be large enough to make any conclusions. This means we can reject option B and C as these options are dealing with small sample sizes.

Now, we have to pick the right option out of A and D only

We know that the central limit theorem suggests that as the sample size increases, or it becomes large enough then the sampling distribution of the mean is said to be approximately normally distributed, irrespective of the individual sample distribution in the population.

This means there is no necessity for the population to be normally distributed while applying the central limit theorem, So option A can also be rejected.

Thus, only option D is the correct answer

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 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.
The central limit theorem states that: Populations with more than 30 observations are approximately normally distributed....
The central limit theorem states that: Populations with more than 30 observations are approximately normally distributed. As the sample size increase, a sampling distribution will look more and more like the population. As long as the sample size collected is at least 30, the variable of interest will always be approximately normally distributed. A skewed-left population can never be a sampling distribution that is approximately normally distributed. For sufficiently large random samples, the sampling distribution of the sample mean is...
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.
The Central Limit Theorem implies that [Select the correct answers - There may be more than...
The Central Limit Theorem implies that [Select the correct answers - There may be more than one correct answer. Negative marking will apply for incorrect selections.] (a) All variables have bell-shaped sample data distributions if a random sample con- tains at least about 30 observations. (b) Population distributions are normal whenever the population size is large. (c) For large random samples, the sampling distribution of y ̄ is approximately normal, regardless of the shape of the population distribution. (d) The...
1. Are the following statements TRUE or FALSE?: (a) According to the Central Limit Theorem, given...
1. Are the following statements TRUE or FALSE?: (a) According to the Central Limit Theorem, given a large sample size (N > 30), then a normal probability plot of the same data would necessarily follow a straight line. (b) A 95% confidence interval for a population mean that does not include zero would also mean that a hypothesis test on the same data would yield a significant result at the .05 level. (c) The mean of a t-distribution with 5...
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 ?
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.
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.
(05.02 LC) The Central Limit Theorem says that when sample size n is taken from any...
(05.02 LC) 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? (4 points) I. The distribution of the sample mean is exactly Normal. II. The distribution of the sample mean is approximately Normal. III. The standard deviation is equal to that of the population. IV. The distribution of the population is exactly Normal. a I and...
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?)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT