Degrees of freedom and confidence interval width. As the degrees of freedom increase, the t distributions get closer and closer to the z (N(0, 1)) distribution. One way to see this is to look at how the value of t* for a 95% confidence interval changes with the degrees of freedom.
Make a plot with degrees of freedom from 2 to 100 on the x axis and t* on the y axis. Draw a horizontal line on the plot corresponding to the value of z* = 1.96. Summarize the main features of the plot.