The Central Limit Theorem is important instatistics.Group of answer choicesa-The central limit theorem states that if asample of data is large enough, the samplingdistribution of the sample mean isapproximately normal, regardless of theshape of the population.b-The central limit theorem states that whena sample size is large, the population isapproximately normal.c- The central limit theorem states that thesampling distribution of the sample mean isapproximately normal whenever thepopulation is large enough.d-lf a representative sample of observationsis drawn from a normally shaped population,the sampling distribution of the samplemean will follow a normal distributionregardless of the sample's size.

We have to define the correct definition of Central limit theorem

Answered: The Central Limit Theorem is important…

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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The Central Limit Theorem is important in statistics because for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. for any sized sample, it says the sampling distribution of the sample mean is approximately normal. for a large n, it says the population is approximately normal.
The central limit theorem states that as sample size increases, the sampling distribution of the mean becomes-- more normally distributed more normally distributed less normally distributed but more leptokurtic less normally distributed but more leptokurtic more shaped like the population distribution more shaped like the population distribution smaller than the population mean
The central limit theorem states that if all possible random samples of sizeNare drawnfrom a population with a mean ofμ ̄Xand a standard deviation ofσ ̄X, then asNbecomeslarger, the sampling distribution of sample means becomes approximately (_______) with a mean of (______) and a standard deviation of (______). Fill in the blanks
One of the properties of the central limit theorem (for all situations) is that if the sampling population is not normally distributed , then the sampling distribution will be approximately normally distributed, provided that the sample size is at least 30. True or False
Which of the following statements is not consistent with the Central Limit Theorem? A) The Central Limit Theorem applies to non-normal distributions. B) The Central Limit Theorem indicates that the mean of the sampling distribution will be equal to the population mean. C) The Central Limit Theorem indicates that the sampling distribution will be approximately normal when the sample size is sufficiently large. D) The Central Limit Theorem applies without regard to the size of the sample.
Which of the following are correct general statements about the central limit theorem? Select all that apply 1. The accuracy of the approximation it provides, improves when the trial success proportion p is closer to 50% 2. It specifies the specific mean of the curve which approximates certain sampling distributions. 3. It is a special example of the particular type of theorems in mathematics, which are called Limit theorems. 4. It specifies the specific standard deviation of the curve which approximates certain sampling distributions. 5. It’s name is often abbreviated by the three capital letters CLT. 6. The accuracy of the approximation it provides, improves as the sample size n increases. 7. The word Central within its name, is mean to signify its role of central importance in the mathematics of probability and statistics. 8. It specifies the specific shape of the curve which approximates certain sampling distributions.
Which of the following is NOT a condition that ALWAYS has to be satisfied to apply the Central Limit Theorem to the sample mean? a) The sample size must be larger than 30 b) There are no obvious outliers in the sample if the sample size is less than 30 c) There are no extreme outliers in the sample if the sample size is at least 30. d) The sample observations are independent.
1. The Central Limit Theorem allows for a researcher to: a. estimate the sampling distribution of a sample statistic, but only if the researcher takes many samples of the same size from the same population. b. estimate the sampling distribution of a sample statistic using the results from one sample taken from the population of interest. c. observe the true, population-level values of the quantity being estimated. d. ensure that the study results are scientifically useful. 2. Which of the following is not a property of a theoretical sampling distribution? a. As the size of the samples the statistics in the sampling distribution are based on increases, the center of the sampling distribution gets closer to the true values of the quantity being estimated. b. As the size that each statistic in the sampling distribution comes from increases, the variation in the values in the sampling distribution decreases. c. The characteristics of the sampling distribution are known, and its…
Which of the following is guaranteed by the central limit theorem? The sampling distribution of certain classes of statistics will always be normally distributed regardless of the shape of the parent population. As sample size increases, the sampling distribution of x-bar will more closely approximate the normal curve when the sampled population has a nonnormal shape. The sampling distribution of x-bar is always normally distributed. The sampling distribution of x-bar will always have the same shape as the sampled population.
Mario made a claim that 95% of college male students in their school join triathlon. His friend, Baste, finds this hard to believe and decided to check the validity of such claim, so he took a random sample and found out that 75 out of 90 had joined the race. 1. What is the population proportion? 2. What is the sample proportion? 3. Is the sample large enough to use the Central Limit Theorem?
When using the central limit theorem for means with n = 60, it is not necessary to assume the distribution of the population data is normally distributed. True False
3. The Central Limit Theorem states that the mean of the sampling distribution of the sample mean is A. larger than the population mean. B. exactly equal to the population mean. C. equal to the population mean divided by the square root of the sample size. D. close to the population means if the sample size is large.

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