Launch the Sampling Distributions applet for this section of your text.Create a thread and answer the following questions in your new discussion post. For a population with a Right skewed distribution, generate a sample distribution of (n = 5) and hit the 1 time button. You will see 5 random data points are chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1 time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original right skewed distribution? How does it compare to the original mean and standard deviation of the population?Hit Reset and repeat for a population with a Uniform distribution, generate a sample distribution of (n = 5) and hit the 1 time button. You will see 5 random data points are chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1 time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original uniform distribution? How does it compare to the original mean and standard deviation of the population? Hit Reset and repeat for a population with a Custom distribution. Try to draw a distribution that is not even close to being Normal. Generate a sample distribution of (n = 5) and hit the 1 time button. You will see 5 random data points are chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1 time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original distribution? How does it compare to the original mean and standard deviation of the population? For your custom distribution, share the population mean and standard deviation as well as the mean and standard deviation of the 1000 sample means. How does the value calculated using the formula compare to the standard deviation of the 1000 sample means?What if we did repeated samples of size n=30? What would have been the standard deviation of the sample means for your custom distribution?Explain the Central Limit Theorem in your own words within the context of what you did for this discussion.

Answered: Explain the Central Limit Theorem in…

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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Launch the Sampling Distributions applet for this section of your text.

Create a thread and answer the following questions in your new discussion post.

For a population with a Right skewed distribution, generate a sample distribution of (n = 5) and hit the 1 time button. You will see 5 random data points are chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1 time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original right skewed distribution? How does it compare to the original mean and standard deviation of the population?
Hit Reset and repeat for a population with a Uniform distribution, generate a sample distribution of (n = 5) and hit the 1 time button. You will see 5 random data points are chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1 time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original uniform distribution? How does it compare to the original mean and standard deviation of the population?
Hit Reset and repeat for a population with a Custom distribution. Try to draw a distribution that is not even close to being Normal. Generate a sample distribution of (n = 5) and hit the 1 time button. You will see 5 random data points are chosen and the mean and standard deviation of that sample are shown. Keep hitting the 1 time button many times and look at the shape of the distribution that falls out. Now hit the 5 times button to do 5 samples at a time. What distribution do you notice taking shape? Hit the 1000 times button and see what happens. How does it compare to the original distribution? How does it compare to the original mean and standard deviation of the population?
For your custom distribution, share the population mean and standard deviation as well as the mean and standard deviation of the 1000 sample means. How does the value calculated using the formula compare to the standard deviation of the 1000 sample means?
What if we did repeated samples of size n=30? What would have been the standard deviation of the sample means for your custom distribution?
Explain the Central Limit Theorem in your own words within the context of what you did for this discussion.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Central Limit Theorem:
The inspecting conveyance of test means will become typical in shape as test size increments for any factor, in any event, when the variable isn't regularly conveyed across the populace.
Whenever N is huge, the mean of the examining dispersion will approach the populace mean, and its norm deviation or standard mistake of mean will be sigma/sqrt N. It is significant in sense that it eliminates the condition that the variable is ordinarily disseminated in the populace.

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