Use this diagram to show how the t-value for a 95% CI depends on the sample size.
Mention that the degrees of freedom, (n - 1), is used to look up the t-value. Note that...
- The t-value for 1 d.f. is too large to display on the graph.
- When d.f. > 100, the t-value is just under 2.0.
- Indeed, for d.f. = 100,000, the t-value is 1.960.
- The value 2.0 is a reasonable approximation for d.f. > 30.