Question

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately Select one: A. normal because is always approximately normally distributed B. normal because the sample size is small in comparison to the population size C. normal because of the central limit theorem D. None of these alternatives is correct.

Answer 1

Option ( C ) normal because of the central limit theorem is the correct option .

I central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size (n), and regardless of the population's actual distribution shape.

Putting it on another way, CLT is a statistical premise that, given a sufficiently large sample size from a population with a finite level of variance, the mean of all sampled variables from the same population will be approximately equal to the mean of the whole population. Further more, these samples approximate a normal distribution, with their variances being approximately equal to the variance of the population as the sample size gets larger.

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