Question 89:

Asked on February 22, 2008

1

Answer:

No answer provided yet.Like many things, it depends. Two of the most common applications of using the t-statistic are when comparing two sample means (the t-test) and creating a confidence interval around the sample mean. Usually, the t-statistic is used when computing a statistic on a sample rather than the entire population of whatever is being studied. It’s rarely the case that people have all the data from a population, so the t-statistic is used a lot. Another nice property of the t-statistic is that as your sample size gets larger and larger, the t-statistic and the z-statistic become increasingly the same.

For example, if you were computing a confidence interval around a mean and your sample size was 10, the t-statistic is 2.26 and the z-statistic is 1.96 for a two-sided 95% confidence interval. At a sample size of 100 the t-statistic is 1.98 and at 500 is 1.96. The difference between the two becomes infinitesimally small and they theoretically equal each other when the sample size is infinity.