Question: Tables show that the 95% critical values for some t distributions are (to 2 dp) as follows:

df 6 9 12 20 30

critical values ±2.45 ±2.26 ±2.18 ±2.09 ±2.04

Use statistical tables or the TINV function in EXCEL to find the critical values for the t distribution with the following degrees of freedom

5 8 15 18 24 60 120

Combine the two tables, and hence argue that these critical values approach ±1.96 as the number of degrees of freedom tends to infinity. Briefly comment on why would we should expect ±1.96 to be the limit here.

Investigate the behaviour of the 99% critical values for these degrees of freedom, and comment on the limits in this case.