Confidence Interval for a Population Mean, when the Distribution is Non-normal

When the distribution is normal, we use the z-statistic when the population variance is known and we use t-statistic when the population variance is unknown.

However, when the distribution is not normal, we cannot create a confidence interval if the sample size n<30.

If sample size >30 and the distribution is non-normal then:

  • If population variance is known, we use z-statistic
  • If population variance is unknown, we use t-statistic. Even z-statistic is acceptable, but t-statistic is more common.

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