STATISTICAL TECHNIQUES AND TOOLS
CONCEPT OF POINT AND INTERVAL ESTIMATION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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True
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False, it’s small
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Either A or B
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None of the above
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Detailed explanation-1: -The central limit theorem states that the sampling distribution of the mean will always follow a normal distribution under the following conditions: The sample size is sufficiently large. This condition is usually met if the sample size is n ≥ 30.
Detailed explanation-2: -The central limit theorem applies to almost all types of probability distributions, but there are exceptions. For example, the population must have a finite variance. That restriction rules out the Cauchy distribution because it has infinite variance.
Detailed explanation-3: -Therefore, the central limit theorem indicates that if the sample size is sufficiently large, the means of samples obtained using a random sampling with replacement are distributed normally with the mean, µ, and the variance, 2 n, regardless of the population distribution.