 # Under what circumstances is a t statistic used instead of a z -score for a hypothesis test? ### Essentials of Statistics for The B...

9th Edition
Frederick J Gravetter + 2 others
Publisher: Cengage Learning
ISBN: 9781337098120 ### Essentials of Statistics for The B...

9th Edition
Frederick J Gravetter + 2 others
Publisher: Cengage Learning
ISBN: 9781337098120

#### Solutions

Chapter
Section
Chapter 9, Problem 1P
Textbook Problem

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

Expert Solution
To determine

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

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.

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