Suppose that a sample of size n=3 is selected from a population of four value 4,8,0, 12.(1) Find the population distribution.(2) Find the mean and standard deviation of the population distribution.(3) Suppose that the sampling is without replacement.(a) Find the sampling distribution of the sample mean.(b) Find the mean of this sampling distribution.(c) Find the standard deviation of this sampling distribution. (Calculatestandard deviation: https://www.youtube.com/watch?v=YMbt5rYzp-Q)(d) Compare the mean and standard deviation of this sampling distributionwith those of the population. Summarize your findings.(e) Letp = the proportion of values in the population that equal O. Let p bethe proportion of values in the sample that equal O.(e1) Find the sampling distribution of the sample proportion.(e2) Find the mean of this sampling distribution.(e3) Find the standard deviation of this sampling distribution.(e4) Compare the mean of this sampling distribution with the populationproportion p. Summarize your findings.(4) Suppose that the sampling is with replacement,(a) Find the sampling distribution of the sample mean.(b) Find the mean of this sampling distribution.(c) Find the standard deviation of this sampling distribution.(d) Compare the mean and standard deviation of this sampling distributionwith those of the population. Summarize your findings.(e) Letp=the proportion of values in the population that equal O. Let p bethe proportion of values in the sample that equal 0.(e1) Find the sampling distribution of the sample proportion.(e2) Find the mean of this sampling distribution.(e3) Find the standard deviation of this sampling distribution.(e4) Compare the mean of this sampling distribution with the populationproportion p. Summarize your findings.(5) Suppose that the sample consists of the three numbers 4, 0, and 8. Now, treatthis sample as a new population. Select, with replacement, three values from thisnew distribution and call this new sample a bootstrap sample. There are manydifferent bootstrap samples.(a) What is the probability of getting each of the bootstrap samples?(b) Calculate the mean of each bootstrap sample. Then, all of these means,along with the probabilities just obtained, gives a distribution which can be usedas an approximation to the sampling distribution of the sample mean. Thisdistribution is called the bootstrap distribution of the sample mean. Create atable for it.(c) What is the mean of this bootstrap distribution?(d) Compare this mean with the sample mean (the mean of the originalsample), what conclusion can you possibly draw?Remark: How many different bootstrap samples are possible? There is a generalresult we can use to count it: Given N distinct items, the number of ways ofchoosing n items with replacement from these items is given by(N+n-12-1).nabove, we have N= 3 and n = 3. So, there are totally. To count the number of bootstrap samples we discussed(³ + 3 − ¹) = (3)= 10 bootstrap samples.Submission: Submit an R Markdown that generates a neat html output. The htmlfile should also be submitted. Don't use rpubs.com.

Answered: Suppose that a sample of size n-3 is…

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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Let a population consist of the values 7 cigarettes, 20 cigarettes, and 21 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?
please state the approximate distribution of the sample mean
The annual salary for one particular occupation is normally distributed, with a mean of about $134,000 and a standard deviation f about $21,000. Random samples of 35 are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution. The mean is μ =, and the standard deviation is = (Round to the nearest integer as needed. Do not include the $ symbol in your answers.)
The weight in kilograms of the citizens of Fredonia has a mean of 50 kg and standard deviation of 24 kg (a) Find the mean of the sampling distribution of the sample mean. (b) Find the standard deviation of the sampling distribution of the sample mean.
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Image has all the data
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A variable of two populations has a mean of 30 and a standard deviation of 18 for one of the populations and a mean of 30 and a standard deviation of 32 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 16, respectively, find the mean and standard deviation of X₁ -X₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁-X₂ is (Round to four decimal places as needed.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. OA. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x₁-x₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. B. No, the formulas for the mean and standard deviation of…
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