t-statistic vs. z-statistic

t-statistic:
It can be used when the population variance is unknown for large samples and small samples with normally distributed population. Comparing the t-statistic with critical value that comes from Student’s t table.

Critical value from Student’s t table
Look up df=n-1, p=significance for 1-sided test or p=significance/2 for 2-sided test

t-distribution is less peaked and flater tails than normal distribution but move closer at higher degrees of freedom.

z-statistic:
It is based on the standard normal distribution and can be used when population is normally distributed with known variance; also for large samples with unknown variance.

Summary of the applications of z-statisitc and t-distribution

My tips:

• Memorize the following commonly used values (from z-table):
• Confidence Interval Reliability factor
  90% 1.65 ; 95% 1.96 ; 99% 2.58
• Be able to look up Student's table given degrees of freedom and probability in the right tail.