7.121 Degrees of freedom and t*. 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.

1. (a) Make a plot with degrees of freedom from 10 to 100 by 10 on the x axis and t* on the y axis. Also draw a horizontal line on the plot corresponding to the value of z* = 1.96.

2. (b) Summarize the main features of the plot.

3. (c) Describe how this plot would change if you considered a 90% confidence interval.