Topic 5 DQ 1
The first problem we confront in analyzing data is determining the appropriate statistical test.
Under what circumstances is a t statistic used instead of a z-score in a hypothesis test? Give an
example of both a t statistic and z-score.
In statistics, the t-test is a type of statistic that allows the comparison between a sample mean and
population mean. It establishes how significant are the means of the two groups. (Gravetter, et al,
2021). The t-test is used instead of the z-score when the population standard deviation and the
variance are unspecified from the data. It is also appropriate to use the t-test when the size of the
sample is small, which is equal to or less than 30. For example, in a study, a researcher wants to
know how the reaction time is affected by alcohol. So, when performing the effects of alcohol on
people reaction-time, the t-test can be used to measure their reaction when they are drunk and
when they are not. The Z-test allows the research to compare whether two population means are
different. It must be used when the standard deviation is known and the sample is greater than
30. (Meena, 2020). As an example, a study wants to determine in our class if men score an
average of 10 more than women. The standard deviation of both men and women are disclosed
and the sample size is 30 men and 30 women. In this case, the z test must be used instead of a t-
test to make this comparison.
Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Essentials of statistics
for the behavioral sciences (10th ed.). Cengage. ISBN-13: 9780357035528
Meena, Subhash. Hypothesis Testing: Difference between z-Test and t-Test. Analytics Vidhya, 23
Dec. 2020, www.analyticsvidhya.com/blog/2020/06/statistics-analytics-hypothesis-testing-
z-test-t-test.
The first problem we confront in analyzing data is determining the appropriate statistical test.
Under what circumstances is a t statistic used instead of a z-score in a hypothesis test? Give an
example of both a t statistic and z-score.
In statistics, the t-test is a type of statistic that allows the comparison between a sample mean and
population mean. It establishes how significant are the means of the two groups. (Gravetter, et al,
2021). The t-test is used instead of the z-score when the population standard deviation and the
variance are unspecified from the data. It is also appropriate to use the t-test when the size of the
sample is small, which is equal to or less than 30. For example, in a study, a researcher wants to
know how the reaction time is affected by alcohol. So, when performing the effects of alcohol on
people reaction-time, the t-test can be used to measure their reaction when they are drunk and
when they are not. The Z-test allows the research to compare whether two population means are
different. It must be used when the standard deviation is known and the sample is greater than
30. (Meena, 2020). As an example, a study wants to determine in our class if men score an
average of 10 more than women. The standard deviation of both men and women are disclosed
and the sample size is 30 men and 30 women. In this case, the z test must be used instead of a t-
test to make this comparison.
Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Essentials of statistics
for the behavioral sciences (10th ed.). Cengage. ISBN-13: 9780357035528
Meena, Subhash. Hypothesis Testing: Difference between z-Test and t-Test. Analytics Vidhya, 23
Dec. 2020, www.analyticsvidhya.com/blog/2020/06/statistics-analytics-hypothesis-testing-
z-test-t-test.
