In this problem, you will explore the relationship between the sampling distribu

Question

In this problem, you will explore the relationship between the sampling distribution of sample mean and the population distribution and understand the Central Limit Theorem. This problem does not require a specific data set, so just open a blank spreadsheet on StatCrunch.

(a) For a non-normally distributed variable,

(Instruction: Under Applets – Sampling distributions – under “Population”, choose any variable that is not bell shaped, enter any mean and standard devotion or just use the default values; leave others alone, click “Compute”.)

Vary sample size for n = 2, n = 5, and n = 30. You can click “1 time”, “5 times”, or keep clicking “1000 times” at the top to obtain more samples. Copy and paste the screens with the graphs you obtained for n=2, n=5, and n=30, below. Comment on the shape, mean, and standard deviation for the population distribution (first graph) AND the sampling distribution of sample mean (third graph). Is the simulation result consistent with the Central Limit Theorem? Briefly explain your answer.

Explanation / Answer

The less normal the population, the larger the sample you need. Though, having said that, the Central Limit Theorem often works surprisingly well. For this population, the sampling distribution wasn't wildly non-normal even for n=5, so you could imagine that a sample size of n=30 or so would be all right.

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