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Question 802:



No answer provided yet.Typically, the z-score or z-statistic is used in statistical tests when the population standard deviation is known and the sample sizes is reasonably large (>30).  Therefore, the t-statistic is used when we have small samples and when the population standard deviation is not known.

In practice, we rarely know the population standard deviation. It is usually only known when we work with things like IQ scores, heights, weights, GRE/SAT scores or other standardized tests in which we have measured all members of a population.

The t-statistic takes into account sample size and approaches the z-score (which comes from the normal distribution) so you the best approach is to usually use the t-statistic and know that when your sample sizes get large ( above 50) the difference between the z and t is very small and would likely lead to identical conclusions.

Examples of research studies in which the t statistic is more appropriate since the population standard deviation is unknown
  1. is there a difference in response times between groups 20 drivers who are talking on a cell phone and those who aren't.
  2. Do students perform better on math tests (dependent variable is grade on math tests) who receive a new teaching method versus those who receive the standard method.

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