- T-distribution. The t-distribution looks very similar to the Normal distribution we have studied many times in class. You can calculate the critical value t* from table D in your book or by using Statcrunch. To calculate the critical value t* for a 90% confidence interval for an SRS of size n=12 observations you would do the following:
- Go to "Stat" → "Calculators" → "T"
- For: "DF" (insert 11) (note: The degrees of freedom are n-1)
- Then to the right of the "=" sign (insert .05) (Note: Recall that the .05 comes from the formula
Thus, the critical value t* for a 90% confidence interval for an SRS of size n=12 observations gives you 1.796 (or -1.796 depending on if you used a ">" or "<" sign on the calculator).
Question #1: What is the critical value t* for and SRS of size n=30 with an 80% confidence level?
Question #2: When would we use the t* critical value instead of the z* critical value? (Hint: The answer is based on a condition of σ)