#3.1)When computing confidence intervals, the critical quantile is always derive

Question

#3.1)When computing confidence intervals, the critical quantile is always derived from the theoretical (simulated) t-distribution, which assumes normality.

#    As you discovered in 2.4, the actual distribution of t-scores can be very different from the theoretical one, depending on the population distribution.

#    If we ignore the fact that the population may be non-normal, and compute confidence intervals in the usual way,

#          what will happen to the probability coverage (i.e. accuracy) of the confidence intervals? (1pt)

Explanation / Answer

If the data distribution is not normal and the data is not skewed, then for sufficiently large sample, then we can assume approximately Normal distribution.

But if the data is skewed and we have small sample, then we can't assume Normal approximation and we have to go for non-parametric confidence interval.

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