Describe the way in which the sampling distribution changes

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Reference no: EM132397374

Assignment

R is necessary for the next portion. We will examine the sampling distribution of the mean in two cases: one where the population distribution is not normal, and one where it is. All of the coding has been done for you and is in the file "CLT_illustration.R". Run it line by line and respond to the following prompts. The variables referred to here are defined in the supplied R script.

1. (a) Describe the population distribution of X in terms of shape and skew.

(b) Describe the steps in creating a sampling distribution of X‾.

(c) Look at the sampling distribution of X‾ when n = 1. Is it normal? How about n = 5? Gradually increase n until the sampling distribution looks Normal.

(d) Describe the way in which the sampling distribution changes as we increase the sample size. Do we need to invoke the Central Limit Theorem to achieve the Normality of X‾?

2. (a) Describe the population distribution of Y in terms of shape and skew.

(b) Look at the sampling distribution of Y‾ when n = 1. Is it normal? How about n = 5? Gradually increase n and see how the distribution changes.

(c) Describe the way in which the sampling distribution changes as we increase the sample size. Do we need to invoke the Central Limit Theorem to achieve the Normality of Y‾?

3. (a) Describe the population distribution of Z in terms of shape and skew.

(b) Predict what will happen to sampling distribution of Z‾ if we start with n = 5 and we allow sample size to increase.

(c) Do we need to invoke the Central Limit Theorem to achieve the Normality of Z‾? Is the story of the sampling distribution of Z‾ more similar to that of X‾ or Y‾ ?

Attachment:- CLT_illustration.rar

Reference no: EM132397374

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