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.