23 June, 12:54

# Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample data values looks more and more Normal." Is the student right? Explain your answer. (Select all that apply.) a) The central limit theorem says that the histogram of sample means (from many large samples) will look more and more Normal. b) The central limit theorem says that the histogram of sample data values (from a very large population) will look more and more Normal. c) The histogram of the sample data values will look more and more Normal. d) The histogram of sample data values will look like the sample it was taken from. e) The histogram of the sample data values will look like the population distribution, whatever it might happen to be.

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1. 23 June, 13:17
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The student is wrong

a. The central limit theorem says that the histogram of sample means (from many large samples) will look more and more Normal.

e. The histogram of the sample data values will look like the population distribution, whatever it might happen to be.

The sampling distributions of means of large sample size is always normal when approximated. It doesn't matter whether the population is normal or it is not, as long as the population is above 30 (30 is considered large enough), then the sampling distribution of means will be approximately normal.

Also, as a general behaviour of the histogram, the central limit theorem states that irrespective of the shape the population distribution takes, the sampling distribution of the sample means approaches a normal distribution as the sample size will get bigger.