Chapter 8.3, Problem 31BB

Finding Critical t Values When finding critical values, we often need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating $\text{t = }\sqrt{\text{df }\cdot \text{ (}{{\displaystyle \text{e}}}^{{\text{A}}^{\text{2}}\text{/df}}-1\text{)}}$ where df = n − 1, e = 2.718, A = z(8 · df + 3)/(8 · df + 1), and z is the critical z score. Use this approximation to find the critical t score for Exercise 12 “Tornadoes,” using a significance level of 0.05. Compare the results to the critical t score of 1.648 found from technology. Does this approximation appear to work reasonably well?