Question

In your own words, explain the difference between a t statistic and a z score and include how the t distribution is related to the normal distribution.

Answer 1

The t test statistic is used in the test, when we are not sure that the distribution is normal and also the sample size is small so that the Central limit theorem cannot be applied.

The only difference between the t statistic and the z score is that t statistic is computed by assuming that the underlying data distribution is t distribution while z score for underlying distribution to be normal.

The t distribution is very similar to the normal distribution in the sense that it is symmetric about the mean. But there are some differences as well. The t distribution has fatter tailes and higher peakedness at the center of the distribution which means that the proportion of values lying away from the mean is greater as well as near the mean are greater in case of the t distribution.