Question

Discuss the distinction between z and t statistics. How are they different? Identify the particular quantity that distinguishes them. Is there a particular class of research questions that lend themselves to testing via the z statistic? If so, what are the characteristics of these questions and data?

Answer 1

For Z statistics we need population standard deviation while if population standard deviation is not known then sample size should be large (n>30) while for t statistics we need sample standard deviation with small sample size(n<30)

T distribution have longer Tail than Z statistics

T statistics have degree of freedom while Z statistics don't have degree of freedom.

If the population standard deviation is given then use Z statistics for testing of mean while

If the population standard deviation is not given but sample size is greater than 30 then use Z statistics with sample standard deviation.

While all questions related to proportion use Z statistics.