In a hypothesis test, the claim is us25 while the sample of 34 has a mean of 21 and a population standard deviation of 5.9 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why? Homework Help: 6DE. When to use z and when to use t distribution (DOCX) Out test statistic would be used as the data are normally distributed with an unknown population standard deviation z test statistic would be used as the sample standard deviation is known @ z test statistic would be used as the population standard deviation is known t test statistic would be used as the population standard deviation is unknown