19. Which of the following statements accurately describes the Central Limit Theorem (CLT) and its implicationsfor statistical inference?A. The Central Limit Theorem states that the population distribution is always normal, regardless ofthe sample sizeB. The Central Limit Theorem guarantee that a sample from any population will always have a normaldistributionC. The Central Limit Theorem ensures that the sample standard deviation is equal to the populationstandard deviationD. The Central Limit Theorem is only applicable to small sample sizes and cannot be used for largeE The Central Limit Theorem applies exclusively to populations with a known mean and standarddeviationF. The Central Limit Theorem states that as the sample size increases, the distribution of the samplemean approaches a normal distribution, regardless of the population distribution.

The objective is to interpret the central limit theorem (CLT). The CLT is considered to obtain the…

Answered: 19. Which of the following statements…

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 says that the standard deviation of the sampling distribution of the sample means is (A exactly equal to the standard deviation. (B close to the population mean if the sample size is small close to the population standard deviation if the sample size is large. equal to the population standard deviation divided by the square root of the sample D size.
Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 117 pounds and a standard deviation of 39.4 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined. 4-0 0 = (Round to three decimal places as needed.) Sketch a graph of the sampling distribution. Choose the correct graph below. O A. A 96.7 117 137.3 Q O B. A 340.8 10.2 361.2 Q Q ww ^ A -106.8 10.2 127.2 86.5 117 147.5 O C. O D. Q
Q2. The sampling distribution of means tends toward Normality only when the underlying populations is Normal. This is true of Central Limit Theorem. TrueB. FalseC. None of the above
A large corporation employs 37525 individuals. The average income of all employees is $76294, with a standard deviation of $17726 and is skewed to the right. Consider this to be the population distribution. You are given a data set consisting of the incomes of 140 randomly selected employees. The population mean is μ=μ= The population standard deviation is σ=σ= The sample size is n=n= Since the sample size is relatively large, the Central Limit Theorem tells us that the sample averages should have a sampling distribution that is (skewed to the rightapproximately normal). The sampling distribution of the sample means is centered at the (populationsample) mean. The sampling distribution has a standard deviation of SD=σ√n=SD=σn= . Round to two decimal places.
Write TRUE if the statement is unconstitutionally true, FALSE if otherwise. 1. That the population's distribution could take on any real number like the Normal distribution does is NOT a condition for the Central Limit Theorem
Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributed
Let a population consist of the values 11 cigarettes, 12 cigarettes, and 22 cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population? Calculate the mean absolute deviation for each possible sample of size 2 from the population. Mean Absolute Deviation Sample {11,11} {11,12} {11,22} {12,11} {12,12} {12,22} {22,11} {22,12} {22,22} (Type integers or decimals rounded to one decimal place as needed.) Budget Pi nd Pow....P Enter your answer in the edit fields and then click Check Answer. Clear All Check Answer parts
Which of the following statements about Chebyshev's theorem is correct? B. Chebyshev's theorem states that all data points lie within three standard deviations of the mean in A. Chebyshev's theorem is only applicable to discrete distributions. any distribution. C. Chebyshev's theorem applies only to positively skewed distributions. D. Chebyshev's theorem applies to any distribution, regardless of its shape. E. Chebyshev's theorem is limited to normal distributions only. F. Chebyshev's theorem guarantees that at least 75% of data lie within three standard deviations of the mean in any distribution. 6. If a data set has a standard deviation of 18 and mean of 70, according to Chebyshev's theorem, what is the interval that must contain at least 19% of the data? A 50 to 90 3 B. 55 to 85 C. 20 to 80 D. 40 to 60 E. 35 to 65 F. None of the above Fina
It is believed that the mean value of a variable measured for an entire population of individuals has value µ = 17 and that for the population the standard deviation is σ = 5.69. A sample of size n= 43 is to be taken from the population. According to the central limit theorem, the sampling distribution of the mean is Normal( 43 , 0.872 ) Normal( 17 , 5.692 ) Normal( 17 , 0.872 ) Normal( 43 , 5.692 )
Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution, Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is $249 with a standard deviation of $57, Random samples of size 32 are drawn from this population and the mean of each sample is determined. The mean of the distribution of sample means is
Which of the following descriptions best illustrate the central limit theorem? I. The central limit theorem is used to approximate the distribution of the sample mean over the distribution of the population mean. II. The central limit theorem is used to conclude that the distribution of the sample mean will be normal if the sample size is sufficiently large even if the population is not normally distributed. III. The central limit theorem is used to describe the normality of the distribution of standard deviation taken from a variance that is not normally distributed. a. I and II b. I only c. I, II, III d. II only

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