Use the R. (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? 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 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.

Question

Accepted Answer

Given:
The population consists of four values: 4, 8, 0, 12
A sample of size n=3 is selected from the…