Is the confidence interval affected by the fact that the data appear to be from a population that is not normally distributed? A. Yes, because the sample size is not large enough. B. No, because the population resembles a normal distribution. C. Yes, because the population does not exhibit a normal distribution. D. No, because the sample size is large enough.
Mathematics · College · Thu Feb 04 2021
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The correct answer is C. Yes, because the population does not exhibit a normal distribution. Confidence intervals are typically based on the assumption that the data are normally distributed, especially when the sample size is small. This is because the methods used to calculate confidence intervals often rely on the properties of the normal distribution. If the population is not normally distributed and the sample size is not large enough to invoke the Central Limit Theorem (which states that the sampling distribution of the sample mean will be approximately normal regardless of the population distribution, given a sufficiently large sample size), the confidence interval calculated may not be accurate.