Question

Describe how the shape and standard deviation of a sampling distribution changes as sample size increases. In other words, describe the changes that occur to a sampling distribution according to the Central Limit Theorem. Make sure you describe what a sampling distribution is in your answer. Generate pictures/diagrams to illustrate your thoughts if you would like.

Answer 1

ANSWER:

From given data,

Describe how the shape and standard deviation of a sampling distribution changes as sample size increases. In other words, describe the changes that occur to a sampling distribution according to the Central Limit Theorem. Make sure you describe what a sampling distribution is in your answer. Generate pictures/diagrams to illustrate your thoughts if you would like.

As per the Central Limit Theorem, regardless of the shape and distribution of the population

if the sample size is greater than 30(n>=30),

the distribution of the sample will be

normal and mean will be approximately equal to the population mean and standard deviation of

the sample =(Population Sdt. Deviation)/sqrt(n)

μ=x̅

and

s=σ/√n

Here, if we increase the value of the n the value of the s will decrease and shape of the sampling distribution will more accurate i,e accurate Normal.