378 CHAPTER 7 Hypothesis Testing with One Sample Finding a Critical Value for a Right-Tailed Test Find the critical value t0 for a right-tailed test with a = 0.01 and n = 17. SOLUTION The degrees of freedom are d.f. = n - 1 = 17 - 1 = 16. To find the critical value, use Table 5 with d.f. = 16 and a = 0.01 in the “One Tail, a” column. Because the test is right-tailed, the critical value is positive. So, t0 = 2.583 as shown in the figure. TRY IT YOURSELF 2 Find the critical value t0 for a right-tailed test with a = 0.10 and n = 9. Answer: Page A41 Because t-distributions are symmetric, in a two-tailed test the critical values are opposites, as shown in the next example. Finding Critical Values for a Two-Tailed Test Find the critical values -t0 and t0 for a two-tailed test with a = 0.10 and n = 26. SOLUTION The degrees of freedom are d.f. = n - 1 = 26 - 1 = 25. To find the critical values, use Table 5 with d.f. = 25 and a = 0.10 in the “Two Tails, a” column. Because the test is two-tailed, one critical value is negative and one is positive. So, -t0 = -1.708 and t0 = 1.708 as shown in the figure at the left. You can check your answer using technology, as shown below. EXCEL =T.INV.2T(0.1,25) 1.708140761 A 1 TRY IT YOURSELF 3 Find the critical values -t0 and t0 for a two-tailed test with a = 0.05 and n = 16. Answer: Page A41 EXAMPLE 2 1% Level of Significance t −3 −4 −2 −1 0 1 2 3 4 = 2.583 t0 α= 0.01 EXAMPLE 3 10% Level of Significance t −3 −4 −2 −1 0 1 2 3 4 −t0 = −1.708 = 1.708 t0 1 2 1 2 α= 0.05 α= 0.05
RkJQdWJsaXNoZXIy NjM5ODQ=