Textbook Problem

Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?

To determine

To find: The circumstances where t-statistic is used instead of a z-score for a hypothesis test.

Answer to Problem 1P

The t-statistic is used when the population variance (or standard deviation) is unknown and sample size is small (less than 30)

Explanation of Solution

The t statistic uses the sample variance or standard deviation in place of the unknown population values. Also, t-statistics is used when sample size is small $(<30)$.

The t-statistic is used when the population variance or standard deviation is unknown.

If use a z-score, the information about population mean, sample mean, population standard deviation and sample size is required. Moreover, z-score works well when sample size is large whereas t-score are ideal for small sample size cases.