Question 5.6: Based on the fatigue strength data presented in Example 5.4,......

The confidence interval has the form \overline{X} ± z_{\alpha ∕ 2}s ∕ \sqrt{n}. We will solve for z_{\alpha ∕ 2}, then consult the z table to determine the value of 𝛼. Now \overline{X} = 408.20, s = 72.9, and n = 70. The upper confidence limit of 422.54 therefore satisfies the equation 422.54 = 408.20 + z_{\alpha ∕ 2}(72.9 ∕ \sqrt{70}). Therefore z_{\alpha ∕ 2} = 1.646. From the z table, we determine that 𝛼 ∕ 2, the area to the right of 1.646, is approximately 0.05. The level is 100(1 − 𝛼)%, or 90%.