will a large-sample confidence interval be valid if the population from which th

Question

will a large-sample confidence interval be valid if the population from which the sample is taken is not normaily distibuted? Explain. Choose the oorrect answer below OA No. A small-sap eco fenoe interval is more ? ely to be valid, but as the sample s ze increases, the condence interval wil be affected more and more by the shape of the population deb to O B. No. Confidence intervais require at least an approximately normal population distribution to be valid O C. Yes. Confidence intervals are always valid regardiess of the shape of the population distribution O D. Yes. As long as a sample is sufficiently large that the Central Limit Theorem applies, the confidence interval will be vailid regardless of the shape of the population distribution Click to select your answer ? ", 5 6 8 3

Explanation / Answer

For the given problem the answer is D.

The Central Limit Theorem states that the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30. All the properties of the normal distribution hold true if the sample size is more than 30 irrespective of the shape of the population distribution.

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